My idea has two parts:

Part 1: Add some "trophy" shelves in the Captain's cabin in our ship's interiors.
Part 2: Have additional "trophy" items for personal effects, such as the Vulcan lute, IDIC plaques, paintings of starships, Klingon weapons, or other decorative items. These could be accolade awards, purchased with latinum or other in-game currencies, or even C-Store items.

These new items would work the same as the existing trophies, so they could also be displayed in the Captain's ready room or ship's lounge/mess hall.

Another thought -- make the fish tank in the Federation ready room a floor trophy, so it could be swapped out for other floor items.