If I remember correctly (it's been over ten years since I did all endings), in your first playthrough, you can get two different (but still similar) endings.
Here's how you get them, if you don't prefer to find them out by yourself :
Spoiler
1 - Engage lavos from the end of time or through the black omen
2 - Engage lavos using epoch
After that, when you start a new game +, you basically have to do the game all over again to get to each ending. There will be a permanent warp to lavos that wasn't accessible on the normal playthrough and when you beat lavos through that warp, the different endings happen depending on the progress of the story (often, the ending will show the consequences of not doing the next thing you were supposed to do storywise).
But still, I would recommend doing the whole story again even if there weren't any new endings, since you can see a lot of things and links to story elements that you missed on your first playthrough (anyway, I did miss a lot of references on my first playthrough).
And just so you know, you will probably even have to start a third game using the data of your second playthrough in order to get through the first new ending available which is found by :
Spoiler
beating lavos with Crono only. This can be done when you volunteer to test Lucca teleporter at the beginning of the game.
Have fun!
