Sound like a motherboard issue because install a 4-5-6th cards isn't more difficult than 3.
This mobo MSI Z97 Gaming 5 can easily handle also 7 nvdia card without this behaviour its always when install just the amd drivers and cards.
Don't Scrooge on your psu.... problem solve
Are you just a troll..or what do you think I save on the PSU..? really are you serious ..
Corsair AXi1500 not less not more!
and I asked more for your methods of installing rather than blaming just the hardware..since I really checked it all and just to repeat I can easily run on the same system 7 NV gpus the issue just comes with AMD driver install.