A week or so ago a user asked this question on…
You're analysis is a bit off because you're missing how this all started. He asked the same question on three sites, Mi Yodea, Hermeneutics, and Christianity all at once. None of us noticed at first that he'd done so. The BH one got flagged for migration and somebody sent it over. The C.SE one got flagged as well, but by the time I saw that flag somebody had already commented that it would be a duplicate, so I closed and deleted it with a comment to the OP asking them to ask on one site at a time next time around.
I then flagged the two copies that were on Mi Yodea for a mod to merge, so that site ended up with just once copy. The BH migration stub will eventually go away automatically.
In other words the OP didn't know any better and tried the shotgun approach. For all we know he posted on various online forums as well, but that doesn't really matter. He's been corrected.
I see no indication of a problem now, but if this comes up again and turns into a pattern of abuse then you could flag one of the examples and link to other cases for a moderator to review.
My question is on if there is anything Moderators can do besides closing/deleting repeat questions by the same user?
Nothing is stopping it from happening, but if it does happen as a pattern of abuse rather than a first timer's mistake then moderators could intervene, yes.
Maybe should be another question is: what stops say a user trolling a site and asking the same question over and over or asking repeated questions that aren't real questions according to the help center?
This is a completely different issue and taken care of by other mechanisms. Just use the site as usual. Vote down poorly thought out questions, vote to close ones that don't fit the site guidelines. The system will do its job from there. Too many closed questions from the same user and it does things like prompt them with extra help, then rate limits them, then asks a moderator to intervene. You don't have to worry about that, just use the tools you have: vote up/down, vote to close, flag, etc.