In a Warcraft 3 LAN game, is there any way to save progress more than once per player?
As per the comments:
The one save is per play rather than per map. So after saving, quit, reload and you'll get your save slot back.
This was/is an anti-spam measure because too much saving could cause the game to crash.
While you already know about this, it is your only way.
The UnlimitedSave mod will do this now.
From the description:
This disables the limitation that prevents you from saving more than once. Only downside is, everybody needs to do it, otherwise the client will disconnect if someone saves for the second time.