Chrono Cross; New Game + Discussion

So here's the thing:

I'm a real stickler over the whole "play a game a few times, play it again try to master it" thing. I want to try and get everything, but I don't want to make multiple save files on my memory card! When you start a New Game plus, can you save OVER your clear game save? Or do you HAVE to make a new file? Like, I won't screw myself over if I save over it, will I?

Thanks for your help guys.

While I APPRECIATE your help, the New Game +/Continue + FAQ by Nev didn't cover a single-playthrough character recovery. His FAQ stated that you at least need to start three games, one for Pierre, one for Guile, and one for Nikki. One of those files would have to have ended early with Lynx and Harle in your party to obtain them later. That WAS the FAQ you were referring to, wasn't it?

I suppose my question should have been, "If I save over my clear game, does it still record the information from the previous play through? Or does it cut me off from the characters I've previously unlocked?"

Thanks.