I've stumbled upon the following cases:
Da(spelled this way this word means
Dà(spelled this way this word means
Da'(spelled this way this word means
give (second person imperative form of "to give")
Clearly in this case one needs to distinguish between two verb forms and hence must choose whether to write a grave accent or an apostrophe accordingly in proper writing.
I wonder whether there are other "trichotomous" words like this, or perhaps even "quadrichotomous" ones involving the acute accent as well, involving the use the apostrophe to produce a word having yet another separate meaning. (?)
I did not realize it at first, but perhaps, besides for reasons of disambiguation, another reason why
Da' is written with an apostrophe is that it is a shortened version of
Dai which can also work as a second person imperative in some contexts (e.g.
Dai a Cesare quel che è di Cesare, (literally:
Give Julius Caesar what Julius Caesar owns)). Hence, the apostrophe works just like in the word
po' which is an abbreviation of
poco (not to be confused with
Po which is the name of the longest river entirely contained within Italy and is its only other near homonym) or the definite feminine article
l' which is an abbreviation of the full definite feminine article
la used before nouns starting with a vowel.