I recently started teaching activities in an American institution.
I have had a couple of students asking for extensions for problem sets / project deadlines for medical or family reasons, which is obviously acceptable. More unexpectedly, other students asked for extensions because they also had problem sets, quizzes and projects due for other classes during the same period (end of semester). Note that there is a buffer period between classes and exams, so we are not talking about conflicts with finals here.
I studied in a different country, in a notoriously work-intensive institution, so the idea that having homework for class X would somehow be an excuse to turn in homework late for class Y simply never occurred to me. I feel that no class should have priority over other classes - if it was the case, differences in credits would reflect that (my class is not a "small one" with little credit). Yes, sometimes students have a lot of work - but is it not part of real life too? On the other hand, the fact that students made these requests so openly makes me think that it might be normal here in the US, and I wouldn't want to be more strict than the local standards.
Is there any kind of norm regarding what is considered as an acceptable reason to ask for an extension?