What if Guardians were just one of five sides to choose from? You could choose to be Vex, Cabal, Hive or Fallen. Each side would have three classes equivalent to Titan, Warlock and Hunter.
Imagine they all have a small grasp on the travel so all have space magic, but they all want full control of it!
Patrols would be bigger and more dangerous and another pvp option. Each race would have a planet or moon or enormous ship with their home base.
Raids and strikes that happen to be defended by your side could be explained in many ways or the enemies and bosses change depending on the team entering if the location permits.
There are a lot of fun details to think about. I can't list them all and I'm more curious to read your ideas too.