"Happens with" is a commonly used phrase that indicates an occurrence or an event that goes alongside something else. To diversify your vocabulary and make your writing more interesting, here are some synonyms you can use instead of "happens with": coincides with, accompanies, is accompanied by, goes hand in hand with, is concomitant with, occurs simultaneously with, parallels, co-exists with, is concurrent with, is interwoven with. Using these synonyms can add flavour and interest to your writing. Experiment with them and find the one that best suits the context you are writing in.