Right now I have 2 1070’s and 2 RX 570’s running in one machine using Windows 10. So it is possible. How you get to that point depends on which OS you’re planning to use and how you set it up and install it.
What I did was install nVidia’s drivers while 1 1070 was in the main PCIe slot. I waited until it was fully installed. I installed the second 1070 and booted up the machine and waited until it was seen in the Device Manager and the drivers automatically installed.
I then put in the first RX 570 and installed AMD’s drivers. Once it was done, I put in the second RX 570 and booted up the machine. Once again I waited a few minutes and in the Device Manager the second RX 570 showed up and the drivers were automatically installed. You just simply run 1 miner for each kind. Personally I run dstm’s miner for the nVidia cards and Claymore for the AMD cards. Works well.
Make sure you enable 4G in your BIOS for anything above 3 cards or it may not boot up.