The phrase "go down with" can have various synonyms depending on the context, some of which include "fall ill with", "contract", "suffer from", "be afflicted by", and "catch". These different terms highlight the negative connotation often associated with the phrase, which usually implies the onset of a medical or health-related issue. For example, one might say "He went down with the flu last week and has been in bed ever since." However, it's important to note that "go down with" can also be used to describe a ship sinking or a sports team being defeated, meaning that the appropriate synonym may vary depending on the specific usage.