"Come down with" is a common expression that refers to catching an illness or a disease. It is always useful to have synonyms or alternative words available to improve your writing or speech. Some of the synonyms for "come down with" include: contract, acquire, develop, catch, get, pick up, fall ill, become infected, be stricken with, come down, be taken ill, fall victim to, be struck down by, succumb to, take ill with, fall sick with, or begin to suffer from. Using synonyms for "come down with" can help vary your language and improve your communication skills.