How do you open up a different save file in Pokemon Moon without deleting the other one?

Solution 1:

You cannot start a new save file without deleting the old one. Pokemon games never supported multiple save slots and Sun and Moon are no different. You would have to delete the old save file to start a new game.

Solution 2:

If you go through the process of installing CFW (custom firmware) onto your 3DS, it's possible to have two different save files via the use of a save manager. I am aware that this question is really old, but in case anyone else wants to do it, I'll leave this link here: 3ds.guide

Solution 3:

You can't have two save files. I recommend you just buy Pokemon Sun, because if you have another 3ds, you can trade pokemon to and from pokemon sun and have the chance to complete the entire Alolan Pokedex, considering the fact that each game has different pokemon.