diff --git a/doc/users/next_whats_new/pyplot-register-figure.rst b/doc/users/next_whats_new/pyplot-register-figure.rst
new file mode 100644
index 000000000000..1acc0d0bf767
--- /dev/null
+++ b/doc/users/next_whats_new/pyplot-register-figure.rst
@@ -0,0 +1,58 @@
+Figures can be attached to and removed from pyplot
+~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+Figures can now be attached to and removed from management through pyplot, which in
+the background also means a less strict coupling to backends.
+
+In particular, standalone figures (created with the `.Figure` constructor) can now be
+registered with the `.pyplot` module by calling ``plt.figure(fig)``. This allows to
+show them with ``plt.show()`` as you would do with any figure created with pyplot
+factory methods such as ``plt.figure()`` or ``plt.subplots()``.
+
+When closing a shown figure window, the related figure is reset to the standalone
+state, i.e. it's not visible to pyplot anymore, but if you still hold a reference
+to it, you can continue to work with it (e.g. do ``fig.savefig()``, or re-add it
+to pyplot with ``plt.figure(fig)`` and then show it again).
+
+The following is now possible - though the example is exaggerated to show what's
+possible. In practice, you'll stick with much simpler versions for better
+consistency ::
+
+    import matplotlib.pyplot as plt
+    from matplotlib.figure import Figure
+
+    # Create a standalone figure
+    fig = Figure()
+    ax = fig.add_subplot()
+    ax.plot([1, 2, 3], [4, 5, 6])
+
+    # Register it with pyplot
+    plt.figure(fig)
+
+    # Modify the figure through pyplot
+    plt.xlabel("x label")
+
+    # Show the figure
+    plt.show()
+
+    # Close the figure window through the GUI
+
+    # Continue to work on the figure
+    fig.savefig("my_figure.png")
+    ax.set_ylabel("y label")
+
+    # Re-register the figure and show it again
+    plt.figure(fig)
+    plt.show()
+
+Technical detail: Standalone figures use `.FigureCanvasBase` as canvas. This is
+replaced by a backend-dependent subclass when registering with pyplot, and is
+reset to `.FigureCanvasBase` when the figure is closed. `.Figure.savefig` uses
+the current canvas to save the figure (if possible). Since `.FigureCanvasBase`
+is Agg-based any Agg-based backend will create the same file output. There may
+be slight differences for non-Agg backends; e.g. if you use "GTK4Cairo" as
+interactive backend, ``fig.savefig("file.png")`` may create a slightly different
+image depending on whether the figure is registered with pyplot or not. In
+general, you should not store a reference to the canvas, but rather always
+obtain it from the figure with ``fig.canvas``. This will return the current
+canvas, which is either the original `.FigureCanvasBase` or a backend-dependent
+subclass, depending on whether the figure is registered with pyplot or not.
diff --git a/lib/matplotlib/_pylab_helpers.py b/lib/matplotlib/_pylab_helpers.py
index e3c3d98cb156..05f6d8aa02b3 100644
--- a/lib/matplotlib/_pylab_helpers.py
+++ b/lib/matplotlib/_pylab_helpers.py
@@ -53,6 +53,8 @@ def destroy(cls, num):
         two managers share the same number.
         """
         if all(hasattr(num, attr) for attr in ["num", "destroy"]):
+            # num is a manager-like instance (not necessarily a
+            # FigureManagerBase subclass)
             manager = num
             if cls.figs.get(manager.num) is manager:
                 cls.figs.pop(manager.num)
diff --git a/lib/matplotlib/backend_bases.py b/lib/matplotlib/backend_bases.py
index 4adaecb7f8c0..51db8dc054e5 100644
--- a/lib/matplotlib/backend_bases.py
+++ b/lib/matplotlib/backend_bases.py
@@ -2723,7 +2723,9 @@ def show(self):
             f"shown")
 
     def destroy(self):
-        pass
+        # managers may have swapped the canvas to a GUI-framework specific one.
+        # restore the base canvas when the manager is destroyed.
+        self.canvas.figure._set_base_canvas()
 
     def full_screen_toggle(self):
         pass
diff --git a/lib/matplotlib/backends/_backend_gtk.py b/lib/matplotlib/backends/_backend_gtk.py
index ac443730e28a..ce6982a72526 100644
--- a/lib/matplotlib/backends/_backend_gtk.py
+++ b/lib/matplotlib/backends/_backend_gtk.py
@@ -195,6 +195,7 @@ def destroy(self, *args):
         self._destroying = True
         self.window.destroy()
         self.canvas.destroy()
+        super().destroy()
 
     @classmethod
     def start_main_loop(cls):
diff --git a/lib/matplotlib/backends/_backend_tk.py b/lib/matplotlib/backends/_backend_tk.py
index eaf868fd8bec..3cd349cb9e17 100644
--- a/lib/matplotlib/backends/_backend_tk.py
+++ b/lib/matplotlib/backends/_backend_tk.py
@@ -606,6 +606,7 @@ def delayed_destroy():
         else:
             self.window.update()
             delayed_destroy()
+        super().destroy()
 
     def get_window_title(self):
         return self.window.wm_title()
diff --git a/lib/matplotlib/backends/backend_gtk3.py b/lib/matplotlib/backends/backend_gtk3.py
index 888f5a770f5d..68ba3a329b5e 100644
--- a/lib/matplotlib/backends/backend_gtk3.py
+++ b/lib/matplotlib/backends/backend_gtk3.py
@@ -89,6 +89,7 @@ def __init__(self, figure=None):
 
     def destroy(self):
         CloseEvent("close_event", self)._process()
+        super().destroy()
 
     def set_cursor(self, cursor):
         # docstring inherited
diff --git a/lib/matplotlib/backends/backend_nbagg.py b/lib/matplotlib/backends/backend_nbagg.py
index 4d18e1e9fb88..543454ab25fd 100644
--- a/lib/matplotlib/backends/backend_nbagg.py
+++ b/lib/matplotlib/backends/backend_nbagg.py
@@ -137,6 +137,7 @@ def _create_comm(self):
         return comm
 
     def destroy(self):
+        super().destroy()
         self._send_event('close')
         # need to copy comms as callbacks will modify this list
         for comm in list(self.web_sockets):
diff --git a/lib/matplotlib/backends/backend_qt.py b/lib/matplotlib/backends/backend_qt.py
index 401ce0b0b754..68d89e1990bb 100644
--- a/lib/matplotlib/backends/backend_qt.py
+++ b/lib/matplotlib/backends/backend_qt.py
@@ -664,6 +664,7 @@ def show(self):
             self.window.raise_()
 
     def destroy(self, *args):
+        super().destroy()
         # check for qApp first, as PySide deletes it in its atexit handler
         if QtWidgets.QApplication.instance() is None:
             return
diff --git a/lib/matplotlib/backends/backend_wx.py b/lib/matplotlib/backends/backend_wx.py
index f83a69d8361e..5219042e7971 100644
--- a/lib/matplotlib/backends/backend_wx.py
+++ b/lib/matplotlib/backends/backend_wx.py
@@ -1007,6 +1007,7 @@ def show(self):
     def destroy(self, *args):
         # docstring inherited
         _log.debug("%s - destroy()", type(self))
+        super().destroy()
         frame = self.frame
         if frame:  # Else, may have been already deleted, e.g. when closing.
             # As this can be called from non-GUI thread from plt.close use
diff --git a/lib/matplotlib/figure.py b/lib/matplotlib/figure.py
index 03549dd53bc1..eba873cdc221 100644
--- a/lib/matplotlib/figure.py
+++ b/lib/matplotlib/figure.py
@@ -2642,7 +2642,7 @@ def __init__(self,
         self._set_artist_props(self.patch)
         self.patch.set_antialiased(False)
 
-        FigureCanvasBase(self)  # Set self.canvas.
+        self._set_base_canvas()
 
         if subplotpars is None:
             subplotpars = SubplotParams()
@@ -2996,6 +2996,20 @@ def get_constrained_layout_pads(self, relative=False):
 
         return w_pad, h_pad, wspace, hspace
 
+    def _set_base_canvas(self):
+        """
+        Initialize self.canvas with a FigureCanvasBase instance.
+
+        This is used upon initialization of the Figure, but also
+        to reset the canvas when decoupling from pyplot.
+        """
+        # check if we have changed the DPI due to hi-dpi screens
+        orig_dpi = getattr(self, '_original_dpi', self._dpi)
+        FigureCanvasBase(self)  # Set self.canvas as a side-effect
+        # put it back to what it was
+        if orig_dpi != self._dpi:
+            self.dpi = orig_dpi
+
     def set_canvas(self, canvas):
         """
         Set the canvas that contains the figure
diff --git a/lib/matplotlib/pyplot.py b/lib/matplotlib/pyplot.py
index e916d57f8871..e6c609c2b84a 100644
--- a/lib/matplotlib/pyplot.py
+++ b/lib/matplotlib/pyplot.py
@@ -933,6 +933,10 @@ def figure(
         window title is set to this value.  If num is a ``SubFigure``, its
         parent ``Figure`` is activated.
 
+        If *num* is a Figure instance that is already tracked in pyplot, it is
+        activated. If *num* is a Figure instance that is not tracked in pyplot,
+        it is added to the tracked figures and activated.
+
     figsize : (float, float) or (float, float, str), default: :rc:`figure.figsize`
         The figure dimensions. This can be
 
@@ -1019,21 +1023,32 @@ def figure(
     in the matplotlibrc file.
     """
     allnums = get_fignums()
+    next_num = max(allnums) + 1 if allnums else 1
 
     if isinstance(num, FigureBase):
         # type narrowed to `Figure | SubFigure` by combination of input and isinstance
+        has_figure_property_parameters = (
+            any(param is not None for param in [figsize, dpi, facecolor, edgecolor])
+            or not frameon or kwargs
+        )
+
         root_fig = num.get_figure(root=True)
         if root_fig.canvas.manager is None:
-            raise ValueError("The passed figure is not managed by pyplot")
-        elif (any(param is not None for param in [figsize, dpi, facecolor, edgecolor])
-              or not frameon or kwargs) and root_fig.canvas.manager.num in allnums:
+            if has_figure_property_parameters:
+                raise ValueError(
+                    "You cannot pass figure properties when calling figure() with "
+                    "an existing Figure instance")
+            backend = _get_backend_mod()
+            manager_ = backend.new_figure_manager_given_figure(next_num, root_fig)
+            _pylab_helpers.Gcf._set_new_active_manager(manager_)
+            return manager_.canvas.figure
+        elif has_figure_property_parameters and root_fig.canvas.manager.num in allnums:
             _api.warn_external(
                 "Ignoring specified arguments in this call because figure "
                 f"with num: {root_fig.canvas.manager.num} already exists")
         _pylab_helpers.Gcf.set_active(root_fig.canvas.manager)
         return root_fig
 
-    next_num = max(allnums) + 1 if allnums else 1
     fig_label = ''
     if num is None:
         num = next_num
diff --git a/lib/matplotlib/tests/test_axes.py b/lib/matplotlib/tests/test_axes.py
index c96173e340f7..e0b651095cb5 100644
--- a/lib/matplotlib/tests/test_axes.py
+++ b/lib/matplotlib/tests/test_axes.py
@@ -8223,10 +8223,9 @@ def color_boxes(fig, ax):
     """
     fig.canvas.draw()
 
-    renderer = fig.canvas.get_renderer()
     bbaxis = []
     for nn, axx in enumerate([ax.xaxis, ax.yaxis]):
-        bb = axx.get_tightbbox(renderer)
+        bb = axx.get_tightbbox()
         if bb:
             axisr = mpatches.Rectangle(
                 (bb.x0, bb.y0), width=bb.width, height=bb.height,
@@ -8237,7 +8236,7 @@ def color_boxes(fig, ax):
 
     bbspines = []
     for nn, a in enumerate(['bottom', 'top', 'left', 'right']):
-        bb = ax.spines[a].get_window_extent(renderer)
+        bb = ax.spines[a].get_window_extent()
         spiner = mpatches.Rectangle(
             (bb.x0, bb.y0), width=bb.width, height=bb.height,
             linewidth=0.7, edgecolor="green", facecolor="none", transform=None,
@@ -8253,7 +8252,7 @@ def color_boxes(fig, ax):
     fig.add_artist(rect2)
     bbax = bb
 
-    bb2 = ax.get_tightbbox(renderer)
+    bb2 = ax.get_tightbbox()
     rect2 = mpatches.Rectangle(
         (bb2.x0, bb2.y0), width=bb2.width, height=bb2.height,
         linewidth=3, edgecolor="red", facecolor="none", transform=None,
diff --git a/lib/matplotlib/tests/test_backend_qt.py b/lib/matplotlib/tests/test_backend_qt.py
index 6e147fd14380..5bb81e5c1e2d 100644
--- a/lib/matplotlib/tests/test_backend_qt.py
+++ b/lib/matplotlib/tests/test_backend_qt.py
@@ -215,6 +215,10 @@ def set_device_pixel_ratio(ratio):
         assert qt_canvas.get_width_height() == (600, 240)
         assert (fig.get_size_inches() == (5, 2)).all()
 
+        # check that closing the figure restores the original dpi
+        plt.close(fig)
+        assert fig.dpi == 120
+
 
 @pytest.mark.backend('QtAgg', skip_on_importerror=True)
 def test_subplottool():
diff --git a/lib/matplotlib/tests/test_backends_interactive.py b/lib/matplotlib/tests/test_backends_interactive.py
index 9f8522a9df4a..671ad8466aee 100644
--- a/lib/matplotlib/tests/test_backends_interactive.py
+++ b/lib/matplotlib/tests/test_backends_interactive.py
@@ -220,19 +220,22 @@ def check_alt_backend(alt_backend):
     fig.canvas.mpl_connect("close_event", print)
 
     result = io.BytesIO()
-    fig.savefig(result, format='png')
+    fig.savefig(result, format='png', dpi=100)
 
     plt.show()
 
     # Ensure that the window is really closed.
     plt.pause(0.5)
 
-    # Test that saving works after interactive window is closed, but the figure
-    # is not deleted.
+    # When the figure is closed, it's manager is removed and the canvas is reset to
+    # FigureCanvasBase. Saving should still be possible.
     result_after = io.BytesIO()
-    fig.savefig(result_after, format='png')
+    fig.savefig(result_after, format='png', dpi=100)
 
-    assert result.getvalue() == result_after.getvalue()
+    if backend.endswith("agg"):
+        # agg-based interactive backends should save the same image as a non-interactive
+        # figure
+        assert result.getvalue() == result_after.getvalue()
 
 
 @pytest.mark.parametrize("env", _get_testable_interactive_backends())
@@ -285,10 +288,13 @@ def _test_thread_impl():
     future = ThreadPoolExecutor().submit(fig.canvas.draw)
     plt.pause(0.5)  # flush_events fails here on at least Tkagg (bpo-41176)
     future.result()  # Joins the thread; rethrows any exception.
+    # stash the current canvas as closing the figure will reset the canvas on
+    # the figure
+    canvas = fig.canvas
     plt.close()  # backend is responsible for flushing any events here
     if plt.rcParams["backend"].lower().startswith("wx"):
         # TODO: debug why WX needs this only on py >= 3.8
-        fig.canvas.flush_events()
+        canvas.flush_events()
 
 
 _thread_safe_backends = _get_testable_interactive_backends()
diff --git a/lib/matplotlib/tests/test_figure.py b/lib/matplotlib/tests/test_figure.py
index c5890a2963b3..5f0e68648966 100644
--- a/lib/matplotlib/tests/test_figure.py
+++ b/lib/matplotlib/tests/test_figure.py
@@ -147,8 +147,6 @@ def test_figure_label():
     assert plt.get_figlabels() == ['', 'today']
     plt.figure(fig_today)
     assert plt.gcf() == fig_today
-    with pytest.raises(ValueError):
-        plt.figure(Figure())
 
 
 def test_figure_label_replaced():
diff --git a/lib/matplotlib/tests/test_pyplot.py b/lib/matplotlib/tests/test_pyplot.py
index 55f7c33cb52e..44555a333a8c 100644
--- a/lib/matplotlib/tests/test_pyplot.py
+++ b/lib/matplotlib/tests/test_pyplot.py
@@ -471,6 +471,30 @@ def test_multiple_same_figure_calls():
     assert fig is fig3
 
 
+def test_register_existing_figure_with_pyplot():
+    from matplotlib.figure import Figure
+    # start with a standalone figure
+    fig = Figure()
+    assert fig.canvas.manager is None
+    with pytest.raises(AttributeError):
+        # Heads-up: This will change to returning None in the future
+        # See docstring for the Figure.number property
+        fig.number
+    # register the Figure with pyplot
+    plt.figure(fig)
+    assert fig.number == 1
+    # the figure can now be used in pyplot
+    plt.suptitle("my title")
+    assert fig.get_suptitle() == "my title"
+    # it also has a manager that is properly wired up in the pyplot state
+    assert plt._pylab_helpers.Gcf.get_fig_manager(fig.number) is fig.canvas.manager
+    # and we can regularly switch the pyplot state
+    fig2 = plt.figure()
+    assert fig2.number == 2
+    assert plt.figure(1) is fig
+    assert plt.gcf() is fig
+
+
 def test_close_all_warning():
     fig1 = plt.figure()
 

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