So, how would one grow a competitor at this point? Appeal to underserved users?
If you wanted to substantially undercut Facebook, there are only three possibilities.
1) Facebook drops the ball. Basically they screw-up their platform big time, in any number of ways, and make the product so incredibly bad people are desperate to leave. Then you have to have the right product at the right time to catch that exodus, vs other competitors like Google etc.
2) Technology inflection erodes Facebook. For example, had they continued to ignore mobile, they would have died like MySpace. Zuckerberg's move to heavy-mobile was equivalent to Bill Gates's call to arms regarding the Internet tidal wave memo in 1995 [1]. Zuckerberg is young enough and still at peak motivation (seemingly), it'll be very hard to catch him fully off guard on a major inflection.
3) Take a category of audience away and expand it. ie knock down the first bowling pin, one that you can hold and grow outward from. It's key that you be able to hold the ground you take. College students are the obvious target still and always will be. Facebook is very much not cool at this point, but Instagram still is (mostly), that enabled Facebook to kill Snapchat and retake the ground they lost. This third one is always viable and very hard sustain, there will always be a strong/tempting argument for selling at a high price after achieving success in taking ground (eg if Snapchat had sold for $10b or $20b to Facebook instead of going public). The monopoly will almost always pay up to continue their dominance, in the Standard Oil model, so far as they can and avoid anti-trust problems.
[1] https://www.wired.com/2010/05/0526bill-gates-internet-memo/