What does "run with" mean?

Also, run around with. Socialize with; see run around, def. 2.

Take as one's own, adopt; also, carry out enthusiastically. For example, He wanted to run with the idea and go public immediately.

run with the hare, hunt with the hounds. Support two opposing sides at the same time, as in He wants to increase the magazine's circulation along with its price—that's trying to run with the hare and hunt with the hounds. This expression, alluding to being both hunter and hunted at the same time, dates from the 1400s and was already a proverb in John Heywood's 1546 collection.