For any bipartite graph that is the union of three disjoint perfect matchings, a matching of size n-1 with exactly a1, a2, a3 edges from each exists whenever a1+a2+a3=n-1.
Alon, private communication
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Almost-perfect colorful matchings in three-edge-colored bipartite graphs
For any bipartite graph that is the union of three disjoint perfect matchings, a matching of size n-1 with exactly a1, a2, a3 edges from each exists whenever a1+a2+a3=n-1.