One thing that's been spoken about is the lack of variety of missions, they're all either Murder missions or fact-finding missions with neither having much personal stakes to them.
I had an idea.
How about faction side-missions.
Add side-missions given from faction NPCs, in the tower which are collected like Bounties to be completed in the Patrol mode where for example the factions leaders could task you to locate a fallen Guardian of that faction and defend him until extraction. Have it so he/she can be hurt and killed if you don't defend him better., or perhaps Rescue a Guardian that the Fallen or Hive are holding hostage.
The Key thing would be something other than kill for a faceless reason. Side-missions with a personal touch would greatly improve variety
Thoughts
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First you may have wanted to put this in the Feedback/Suggestions section, Second, I think this would be a great addition, with the lore currently pointing toward Guardians building up our forces it would do well for the story to go out and save/help other guardians (other than the current human played), might even add a bit more life to the planets/locations other than filled to the brim with enemies. Could also have a quest that involves guiding a ghost to a location of a known dead guardian and protect him until he revives the guardian.