What happens if I catch an additional outsider?

If you capture several Outsiders, you will have all the shards in your inventory. But the most frustrating thing is that you will not be able to sell the shards. So you will have the shards stuck at your inventory for the rest of the game.

Outsiders will stop appearing only after you finish the mission that comes after you research the shard, but you still won't be able to sell the shards.

Since they are harder to capture that other low level aliens, but have the same weapon (light plasma rifle), I would advise capturing floaters or thin men instead of outsiders if you want the weapons, as they will not appear in your inventory and reduce clutter.

Nothing special happens if you catch more of a single live alien. They just sit quietly in your Containment Facility and do not ask for food. I can't confirm if Outsider Shards appear in your inventory like other aliens' corpses, though.

Outsiders continue to appear on the bridge of UFOs, until they are replaced by another "commanding alien" a plot mission or two later - then you wouldn't be able to encounter them anymore.

You should get an intact weapon for a live capture, at least.