Glad you asked . not a goddang thing.
Lets change that .
How about donating 10% of your max energy for a 1% buff to the base's hull, shields, attack, and defense?
Cap at 25%, only once an attack and lasts the entire length of the attack
How about a limited pop up mission each member of the legion could perform that rewards either a temporary base buff, a base trap, a base repair kit (50k hull repair?), or...?
How about having the one operating defense be able to dock their ship in the base, adding their own attack, defense, shields and hull to the base total?