You can save as many times as you have room on your save device for. During the game the initial file will auto-save in two separate places and each subsequent playthrough for whoever will also use those auto-save files. So if you want a different file for each new player, you need to make a completely different and separate single save file via the menu and possibly make a note of the time shown when you save to be able to identify it later. Therefore each new player can go to and save to their own time file each time they play although the game will auto-continue from the last person who saved. I hope that's clear enough for you!