sorry, who owns the block/garage – as if it’s not you that could add complications and I’d strongly suggest not touching it (I assure you it was fine till X stood on it m’lud then all the garages started leaking), otherwise are you on good terms with other neighbours and have you got their agreement – where I’m going is if you do something and they don’t like it or they are r-soles and they already had leaks they might just become your fault.
(*posted as someone who has experienced sh1tw!t neigbours)
can you hang a sheet of plastic inside so that it drains to the door inside ? (or out of some gap) or divert drips etc into a tank that you can empty every so often or even put the sheeting beneath the roof suitably angled etc