come down with (something)
To become ill. "With" is typically followed by the particular illness. I didn't do much this weekend because I came down with a cold. Our goalie came down with the flu and missed the game.
come down with something
to become or to be sick with some illness. Susan came down with a bad cold and had to cancel her trip. I didn't go to work because I came down with the flu.
come down with
Become ill with, as in The whole family came down with the flu. [Late 1800s]
come down with
To become sick with (an illness): came down with the flu.