No, on one confirmation number, you can only be checked in for 2 segments at a time . .. regardless of where you check in. The ticket counter, skycaps, southwest.com, and mobile.southwest.com all have the same restriction.

It is actually coded into SAAS (our reservations system).

For instance, if you were flying roundtrip all on one day . . .
If your outbound and return are both direct or nonstop, you are able to get both your outbound and return boarding passes (once the return is within 24 hours).

If you have a direct/nonstop outbound, and a connection on the return - you will only get the one outbound BP, as we will not split up boarding passes on a connection - and you cannot get 3 boarding passes.

If you have a connection on the outbound, and direct on the return - you will only get the 2 outbound BP's.

If you are on connections both directions - you will also only get the 2 outbound BPs'.

And, as this whole thread started - if you are on a double-connect, you will only get the first 2 BP's. The third flight will be indicated as "airport checkin required".