Any particular airport?

At LGA, AA currently operates out of Concourses C and D of Terminal B and out of Terminal C (although I think AA plans to consolidate all of its operations in Terminal B; not sure when that's scheduled to happen). They operate an airside shuttle bus between all three locations.

UA operates out of Concourses A and C of Terminal B. DL operates out of Terminals A, C and D. Terminals C and D are connected airside. The separate concourses within Terminal B are not connected airside, except for Concourses C and D using the AA shuttle.

So it's a bit of a hassle, but doable, hopping among the three. The AA airside shuttle is your best bet to avoid re-clearing security, and this will connect you to all AA and most UA and DL flights.