I am interested in how one would modify the below question and answer (what extra notation to use) if routes where more than one base can be considered. For example Main base-->1-->3-->Main or Main base-->2-->1-->3-->Main.
Would the binary variables all need to be changed so that they have 4 subscripts or is there another way? The objective is to minimise the total distance travelled by all ships over all trips taken and should detail what routes are taken, and how many times each type of route is taken.
This depends on how you are going to modify the limit on the number of round trips in the original question. If each ship is going to make one "lap" (leave and return to main base once), you only need three subscripts, with $x_{ijk}=1$ if ship $i$ visits destination $k$ (which could be any base, including main base) immediately after base $j$. If you are going to allow multiple routes for each ship, then you are probably going to want a fourth subscript. I think it's possible to do with the same three subscripts (allowing main base to occur multiple times in a route, not just at the start and end), but the capacity and endurance constraints get slightly trickier and maybe a bit more opaque to the reader.