This neat little trick from FF3US for the SNES still works, and with the addition of the new post-game hidden dungeon, it's even more useful!

Have one of your teams in a multi-team dungeon move onto a Save Point. Next, switch over to one of your other teams. As long as you remain stationary with this second team, you can Save your game, or even better, use a Sleeping Bag or Tent for quick and easy healing!

Should your party move out of place or if you want to save/use a tent again later on, simply switch back to the team on the save point, switch back to the party you wish to save with/heal, remain on one space, then do as you will.