But I can't think of any words on -um that aren't neuter. Most words in -us are masculine and have a plural in -i, a few have a plural in -us as well (but I'm not sure if we regularly use any of those in the modern Western languages).

That is for Latin words of course. The neuter plural in -a is identical in the two languages, and there are some similarities elsewhere, but in general the Latin and Greek declensions are quite different, so you have to be careful with words that look like they might have Latin origins, but have Greek ones instead. Octopus comes to mind.