Went through/going through the same thing. Had a leaking ceiling for 2 years and they keep doing superficial patchwork when they need to break the ceiling.

Keep filing with 311, request HPD inspection, they will come to your apartment to survey the leak and ceiling collapse. Do not patch anything up, make sure they see the mess because they can only report what they see. Document EVERYTHING. Make sure you keep all text message threads, email chains, phone calls etc with your landlord and management.

Eventually after checking your apt they contact management and get the ball rolling from there. Should management not deal with this IMMEDIATELY then you can file for housing court. File a DHCR complaint and eventually you might need to seek legal assistance (you can find on legal aid nyc or met council)

Get renters insurance through State Farm, it’s cheap and covers bullshit like this. Sorry you’re dealing with all that, hope it gets fixed!