My goal: save $ on wiring. Can I use multiconductor cable to run from the main distribution panel to a group of 3KW, 480VAC 3-phase power motors. Currently they are all wired separately, but I've heard of some European companies using multiconductor cable, then splitting to each motor in the group. Are there any US codes against this and will it achieve my goal?

Watch the derating.

Sounds like a feeder and sub-panel may be in order.