I don't think I've ever heard the interconnects affecting each other.
Two things I do hear a difference, first of which, is when separating the red and black sections of speaker cables and separating digital and analog cables. To separate the red and black sections of the speaker cable, you just have to use separate runs of cables. If you are bi-wiring, use a single stereo channel for both the hot and another set of cable for the neutral. This greatly adds more coherency and smoothness in my system. I don't have this set up now since my new speakers have a twisted pair of CAT5 both internally and externally. I might upgrade to separate runs of OTA cables. The other thing I can hear a difference in is separate all cables that are analog and digital related meaning the powercables and interconnects. This is not as perceivable and might just be my brain doing tricks on me.