There are a couple of options available to you matey.
First things first though. Are you looking for a 3rd monitor for just adding more screen estate for desktop work or are you looking for a 3 monitor setup in games? Also could you list your power supply and does your processor have onboard graphics?
If you can give us this info then it will help to offer the best advice based on your specific needs and setup rather than throw a load of suggestions that won't be appropriate.
As you want to use 3 screens for gaming oneoption is to get an identical 570 card and an sli bridge to go sli. I have looked at your motherboard specs and sli is supported but having looked at your PSU specs it seems that it only has 2 x pci-e cables and you will need 4 (2 per card). There are converters that will possibly work but I have never used them so wouldn't like to say go for it or not. If you have the extra cash available then getting a different power supply could be an option or alternatively you could sell your 570 and get a 670 which natively supports 3 screens from 1 card.
Let us know what your budget is and if any of those options are feasible and we will go from there.