You can totally run a second non-crossfire compatible card and have it running independent screens, that is how larger multiscreen setups are done, you only need them to be CF/SLI compatible if you want their powers to combine for driving a single screen. Its not really necessary though since the second screen has a very minimal impact on load for the GPU if all its doing is web browsing. Anything that wouldn't kick the GPU out of 2D mode clocks isn't going to impact your gaming performance.
If you want to though you could pick up something little like an R5 230 and use it to drive a pair of screens while you use the 270x to drive your primary monitor.