Per syllabus, late assignments/exams can be submitted for half-credit but are not guaranteed a careful reading. The reason is simply that I've got a specific time set aside for reading the exams and that’s not compatible with them coming in at different times and dragging things on almost always means that the current material of the course gets short schrift while catching up on the old assignment.
Short of documented emergencies I'd rather not start having to decide which cases of "lots going on" or "not quite done" merit extensions and which ones do not.
My usual advice is to submit a "deposit" by the deadline and keep working and then submit a revised version asap after that knowing that there's a risk of being in that half-credit zone (but safely assuming some consideration given for submitting the deposit).
By "deposit" I mean take what you have got and put it in as presentable a form as possible (it can include things like "note to self: add something about X" or "this section still not clear" or "still to be added: section comparing two authors." Tidying up means doing a quick proofread, formatting a bit, etc.
So, best to turn what you have into its best possible form, submit it by deadline and then revise and submit revised version.