The phrase "happen with" can often be replaced with synonyms that convey a similar meaning, but with different nuances. For instance, "occur with" suggests a more formal or clinical tone, whereas "take place with" implies a more concrete or physical event. Other alternatives for "happen with" include "come about with," "be accompanied by," "coincide with," or "transpire alongside." Each variation brings its own subtle connotations to the phrase, so it's important to choose the one that best suits the context and tone of the sentence.