You can mix cards, but as a general rule you have a lot fewer issues if you stay within the same generation of card (for this purpose, AMD R9 2xx and 3xx cards count as the same generation, as they were mostly just relabeled varients of the same cards with a bit of BIOS mods, ditto the HD77xx/79xx cards to the R9 2xx).
Mixing AMD and NVidia on the same machine can be done, but it's NOT particularty easy and can be a real nightmare to troubleshoot.
NOT RECOMMENDED.
Do NOT try to mix pre-GCN AMD cards (or IGUs) with GCN cards (or IGUs) - they do NOT mix and match at all as the archetectures are totally different and the drivers get totally messed up if you try to do so.
At BEST, you end up not seeing some of the cards (or IGU) 'cause the drivers are working in the "other mode" with the rest.
Not only NOT RECOMMENDED, but specifically JUST DON'T WASTE TIME TRYING TO DO IT.
Thank you very much for this very clear explanation. I guess that putting RX 480 in my R9 380 setup is a bad idea and that R7 370 will work fine. Right ?
I'd recommend against mixing RX480 with any previous cards - they're a major change from anything older and such a mix will likely won't be a particularly stable system.
380 and 370 should play well together.
Trying to run multiple drivers for the same brand is NOT going to work - at best, the "additional" drivers will be ignored, if they're not they ARE going to cause major instability and crashes if the system even comes up at all.
I'm pretty sure you have to run something more recent than the 15.12 Catalyst drivers with a RX480 in the system, as those drivers predate the card by a few months.