Well, I didn't have any issues because they two different card types that use completely different drivers. Where problems start to come up is when you use 2 card types that use similar drivers but are from different series. To my understanding you should stay within the same series type to prevent driver issues. So if you are going to run a 1070, try to pair it up with another '10' series card. A 1050 and a 1070 or 1070 and 1080, etc. If you going to run a 700 series you should pair it with something similar. Or you could get an AMD card to pair with it, like I did, and not have issues. Hope this makes sense.
I do highly recommend replacing that 770 outright, get into the 900 series, at least. I paid $100 on ebay for mine just about two months ago, now. I needed a cheap second GPU to run dual monitors. It's nearly paid for itself. Once SMART coin prices go up, it will have definitely paid for itself.
Us$100 is cheap. Can’t fibd any cheap ones in Singapore.