New Surface Outpost Contract - add on to an existing base?

Solution 1:

You will be able to get it right if the old base attaches to the new module, and not vice versa.

In order to do so, right click a command module or probe core; on the existing base - pick the icon of probe or lander or rover. On the new module, pick the icon of base or space station.

That way, when you dock them together, the game considers the new module to be the "base" (which is new, produced after the contract) and the base a "module" added to the new "base".