A shooter might be hard, but I think you could make ORION: Prelude fit. It’s a little old now, but still fun. You get to shoot dinosaurs and run around big maps.
Other games that I’d recommend: Avorion (build your own spaceships and fight and befriend the galaxy) It’s not technically a shooter, but depending on whether you pick out lasers, electric tasers, machine guns, or rail guns, there is definitely some aspects of moving to avoid enemy fire while plunking them down. [but don’t be like me and just make lots of borg cubes… because cubes are the best!]
Ark: survival evolved (tame dinosaurs and fight the map)
Elden Ring with seamless Coop mod (up to 6 players at once)
War Thunder for plane sim, World of Warships for good ship battles