The k-edge-connectivity augmentation problem with multipartition constraints (kECAMP, for short) is defined by “Given a multigraph G=(V,E) and a multipartition π={V₁,...,V_r} (r≥2) of V, that is, $V = \bigcup_{h = 1}^r V_h$ and V_i∩V_j=∅ (1≤i<j≤r), find an edge set E_f of minimum cardinality, consisting of edges that connect V_i and V_j (i≠j), such that (V,E∪E_f) is k-edge-connected, where a multigraph means a graph, with unweighted edges, such that multiple edges may exist.” The problem has applications for constructing a fault-tolerant network under building constraints, and so on. In this paper, we give a linear time reduction of (σ+1)ECAMP with |π| ≥ 3 to (σ+1)ECAMP with |π|=2 when the edge-connectivity of G is σ and a structural graph F(G) of G is given.