I have 580 8GB, 1070 ti, 1080ti on windows with no issues. 1080 ti is just under 39 mh/s. I tried phoenixminer and wasn't stable at all on my system and had lower hashrate than claymore on the green cards but increased on 580.
You can use two miners simultaneously and independently of each other. Use Phoenix only for AMD cards with the -amd (for example,
PhoenixMiner.exe -pool eu1.ethermine.org:4444 -wal YourEthWalletAddress.WorkerName -amd). Claymore for NVIDIA cards with the parameter -di 0123, where 0123 correspond to NVIDIA cards (for example,
EthDcrMiner64.exe -epool ssl://eu1.ethermine.org:5555 -ewal YourEthWalletAddress -epsw x -di 0123). Run Claymore, remember which numbers correspond to the necessary cards and specify this in the config.