Almost-perfect colorful matchings in three-edge-colored bipartite graphs

We prove that, for positive integers $n,a_1,a_2,a_3$ satisfying $a_1+a_2+a_3=n-1$, it holds that any bipartite graph $G$ which is the union of three perfect matchings $M_1$, $M_2$, and $M_3$ on $2n$ vertices contains a matching $M$ such that $\mathrm{\mid }M\cap M_i\mathrm{\mid }=a_i$ for $i=1,2,$ and $3$. The bound $n-1$ on the sum is best possible in general. Our result verifies the multiplicity extension of the Ryser-Brualdi-Stein Conjecture, proposed recently by Anastos, Fabian, Müyesser, and Szabó, for three colors.