Outside the box, how about inside the box!
What is wrong with good old fashion detective work? You get tips from people you follow them up, you listen to truly public chatter learn who the malcontents are and infiltrate their groups, etc.
All things police and spy agencies have been doing as long as they have existed and it worked without with to a large degree without global privacy shredding mass data collection. Is it likely to be as "effective" my guess is probably not as effective as mass surveillance can be but then again there is little evidence to suggest the the mass surveillance has worked so well, I mean people are still going abroad to meet with terror organizations come home and then sneak bombs on planes; they have just failed to detonate.
Its a question of finding balance: risks, costs, and rewards. The real solution is we need to start getting rational about that.