Given a positive integer $c>1$, for what parameters $(v,k,\lambda,\mu)$ does there exist a $c k$ regular graph on $v$ vertices that can be given an edge coloring with $c$ colors, such that the edges corresponding to each color form a $(v,k,\lambda,\mu)$ strongly regular graph?

For what parameters is the $c$-edge-colored $c k$ regular graph unique up to isomorphism?

Are there any known results, is there any literature on this topic?

This question is related to the questions asked recently at a meeting in Banff, for the case $c=2$.