When it comes to finding synonyms for the phrase "press down", there are several phrases and words that could be used to replace it, depending on the context. For instance, you could use terms like compress, flatten, push down, bear down, force down, squash and tamp down. It could also be substituted with expressions like exert pressure, put weight on, or place a heavy object on top of. Other possible synonyms of "press down" include compact, condense, weigh down, and cram down. Ultimately, the choice of a synonym would depend on the intended meaning and context of the phrase.