Each search is a "leg", but the leg could involve multiple segments, I believe, as long as the award engine supports it. I just used UA and I tests HKG-LAX and I can see the connections. I believe the *A search (which uses ANA) will do the same but it is down for maintenance right now so I can't test.

Note that there is no way to force or only display a specific connection point when the leg contains multiple segments.