Mid and End Game Reraise Criteria

[Cheeseweasel]

I am a selective-aggressive move-in-specialist. I play SNG's. I will push over the top of a raise only if I have AA, KK, or AKs. However, at times this seems to be a bit too tight during middle game and end game when the call goes out the window for many players. What would be your recommendation for minimum hand requirements for pushing over the top during mid game and end game? I prefer answers only from people who are well-versed in all-in and fold equities. Thank you for taking the time to read and reply.