Theme Tip:  One strategy to handle theme answers (the long answers;  always across; sometimes also down) is to start by working out as many “crosses” as possible, i.e. the down clues that cross the long across answers and vice versa.

Theme hint:  Question marks here, indicating some word play.  It’s nothing fancy, as one might expect in a Thursday puzzle, just an answer that fits the two different ways indicated by the clue.

Specific hints:

Lover of Narcissus:  The perfect mate for a self-lover…or something you might hear in a cavern.

Part of the terza rima rhyme scheme:  Don’t worry about the “terza rima” bit: it’s just a simple rhyme scheme.  This type of thing is pretty frequent in xwords and there are really only a few possible alternatives when it comes to rhyme schemes…this one could also be clued as a bygone sports league.

Butt out? :  this is about as racy a clue/answer as the NYT puzzle will get.  Not very racy.

Bush 41 and Bush 43, for two:  Seems like every other president went to the same school.

Corner monopoly square:  Didn’t this come up in the puzzle yesterday?  The NYT rewards “frequent solvers” by repeating answers with only slightly varied cluing.

Orange juice option:  AKA  “Homestyle”