How many excuses are too many? I know we've all had situations with students who seem to have a solid number of excuses not to be in class or get work done.  However, for the most part, it will be only once or twice a semester that I have to deal with any single student for which I'm normally happy to give them the benefit of the doubt with even a modicum of forewarning or evidence of reason (doctor's note, etc).

But I'm pretty much at my wit's end with a student this semester and I'm not entirely how I should deal with it.  The student has missed close to half of class meetings and missed so far both of the exams given so far this semester.   They have had excuses of one sort or another for each absence, but the diversity of them rivals anything Lemony Snicket could hope to write.  But all of them fall within our departmental policy for excused absences so I have to work with the student.  I'll spare details (also for FERPA concerns), but the extra work load it's resulted in has absolutely not been welcome give I'm on a large overload this semester.

When it comes to excused/justified absences, just how many is too many?  And how can one best handle it given departmental or institutional policies that force instructors' hands to be lenient even for cases where, really, a student ought to have withdrawn if they're having so many problems?
Whatever general advice this forum can offer is in my opinion extremely unlikely to offer much insight into your specific situation (though I'd love to be proved wrong by other answers). As you said, this is an issue of departmental policy, so you need to have a good long conversation about the situation with your department chair or grad/undergrad (as applicable) program chair. It is their job to set a policy on such matters that is legal and reasonable and provide you with any resources you need to do your job effectively and without creating an unreasonable workload for you (source: I am a department chair). And of course you will be able to provide them the necessary details that you cannot mention here. Good luck!