If a player visits a secret base of another player, they can get that player's flag. After successfully returning the other player's flag to one's own base, the player's record is updated. The number of flags captured (either from the same "opponent" or several ones) upgrades the player's secret base computer.
Each upgrade changes the graphic slightly (the icons resemble the evolution of personal computer technology) and also allows the player to remove additional boulders from their base using the "Store" option of the "Decorate" menu. This allows more room for decorations to be placed.
Boulders that have been removed cannot be placed back into the base, although they'll reappear if a new base is created.