Given a positive integer $c>1$, for what parameters $(v,k,\lambda,\mu)$ does there exist a $(v,c k, c \lambda, c \mu)$ (simple) strongly regular graph 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 $(v,c k, c \lambda, c \mu)$ strongly 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](http://maths-people.anu.edu.au/~leopardi/Leopardi-ADTHM-graph-question.pdf) asked recently at [a meeting in Banff](https://www.birs.ca/events/2014/2-day-workshops/14w2199), for the case $c=2$.