Chrono Cross' multiple endings were kinda cool in a different way from Chrono Triggers. In your first playthrough there were only two endings after completing the story: one being the true ending, and the other being a sort of "oops, try again" ending. I originally got the oops ending and found it a little frustrating after spending so much time on the game, but I later rectified that.
The real multiple ending shine in Chrono Cross is that on New Game+, you could choose to face the final boss at any point in the story. The story's ending would then be based on what was happening in the game world at that time. I can see why this was saved for NG+, since they wanted you to see the full story and not cut it short, but the ability to choose where the story ends and see how the world would proceed without your further involvement is a pretty nifty idea.