Galaxy Quest is one of my favorite movies, but so much of the movie revolves around a gimmick (Washed up sci-fi TV actors suddenly find themselves on a spaceship built by aliens that thought the TV show broadcast was actual historical footage) that can only be used once. All the character arcs were completed.
Any sequel is probably just going to be limited to being another Star Trek parody.
We now know that the ships and stuff can be real, so they’re filming the new stories in actual space. Galaxy Quest II actually becomes an actual series of “historical documents” recording the actual missions they’re doing, but have to be presented to the human viewers as just another sci-fi series. Hilarity abounds as the production team tries to make reality look just fake enough to pass for a fictional TV show. New fans who used to laugh at the original fans for taking the show too seriously are getting laughed at by the original fans for suggesting that “It’s all real, man!”