Both "save for" and "save" are grammatically correct there, but I believe "save" would generally be preferred. Here, "save/save for" mean the same thing and follow the same rules as "except/except for", and there are a complex set of rules governing when you put the "for" in. The relevant rule in this case (from this website) is"
After words like all, every, no, everything, anybody, nowhere, whole etc., except and except for can both be used with the same meaning,
but people generally leave off the "for" in this case.
If you do not have a word implying "all" or "none", like these, you must include the "for". Another rule is that if the word it is modifying comes after the word "except", you must include the "for". The rules for "except/except for" are quite complex. At some point, I found a complete set of rules for "except" versus "except for" on the web, but all the websites I can find right now don't seem complete.