Applying to a job after just accepting an offer I just accepted an offer after the usual cycle of tenure-track applications starting in December. However, there's another job posting I'm very interested in that was just posted now for some reason(*). Is it possible for me to apply anyway? On one hand I'm just curious to see if I might get interviewed at least, on the other hand I'm pretty happy with the job I accepted, but this second one is closer to home, so I might want to try to negotiate a double position or something (spending half the year at either university). Field is math btw, both are TT positions.
Assuming it is not unreasonable to apply (don't want to get on people's bad side), I assume I should explain the situation in the cover letter. So I guess part of the problem is coming up with a &quot;valid&quot; motivation for applying. If I tell them straight up I only want a double position, they might not consider my application at all(?).
(*) I don't understand why it's posted so late. It also says review will begin immediately - maybe they already have someone in mind?
This is an excellent way to burn bridges at two institutions, do not do it.  The interview process for a TT position is long and daunting for everyone involved.  It is also expensive - even if this was a purely virtual interview cycle.  The sheer number of hours that the hiring committee put in to your application and interview when they could have been doing something else in their busy schedule means that they have a good reason to expect that someone who has accepted the job offer they gave will actually do that job.
If you were offered but did not accept, or were still in the interview round, this would be a very different question.  But since you have accepted the job offer then reneging on what you agreed to will look pretty bad on you.
I can see this going poorly for you in several ways:

You apply to the second position, get it, and then try to negotiate a double-job.  Both institutions would reasonably be confused and upset here, with the second job offer probably being pulled and the first institution probably eying you with suspicion.

You tell the first place what you're doing, and apply anyway.  I expect they will be quite concerned that your intention is to jump ship whenever a slightly more interesting position becomes available.

You tell both places what you're doing right from the outset.  The second institution is unlikely to consider you unless you are amazing at what you do - they want a tenured prof eventually, that's a lifetime committment - and still the first place eyes you suspiciously.


The only way I see this working, and it is not ideal, is for you to apply to the second position, get it, and then leave the first to work at the second.  But, you've just gotten a TT position that you seem to be interested in...why would you do that?