So before the New52, Hawkman (archaeologist/reincarnated warrior/ancient weapon user) led the JSA (the team of the past). Superman (reporter of contemporary events/man with the timeless fighting style) led the JLA (the team at their prime. And Cyborg (scientist/protector of a future generation of heroes/futuristic weapon user) led the Titans/Teen Titans.
They were past, present, and future. They had very different personalities. They still do, actually.
Would you buy a mini-series of these three fighting a threat across different times? It sounds like the ultimate adventure to me.