  Let $G$ be a graph with maximum degree $\Delta(G)$ and maximum multiplicity
$\mu(G)$. Vizing and Gupta, independently, proved in the 1960s that the
chromatic index of $G$ is at most $\Delta(G)+\mu(G)$. The distance between two
edges $e$ and $f$ in $G$ is the length of a shortest path connecting an
endvertex of $e$ and an endvertex of $f$. A distance-$t$ matching is a set of
edges having pairwise distance at least $t$. Edwards et al. proposed the
following conjecture: For any graph $G$, using the palette $\{1, \dots,
\Delta(G)+\mu(G)\}$, any precoloring on a distance-$2$ matching can be extended
to a proper edge coloring of $G$. Gir\~{a}o and Kang verified this conjecture
for distance-$9$ matchings. In this paper, we improve the required distance
from $9$ to $3$ for multigraphs $G$ with $\mu(G) \ge 2$.
