Settlement defence after reactivation, maybe - have to repair the turrets, then run to security and get the turrets online etc. Could tie that in with massacres where you can draw an NPC in to a location using incriminating evidence for capture/takedown.
Can we get some grenade throw indicators? They're more fiddly than the original original Team Fortress, and I didn't think that possible.
As NPCs are usually in short supply, some more drone variety would be nice, maybe some ground based (yes, that probably means "spiders") and the ability to down and e-breach a drone temporarily (another use of overload from suit charger,) sending it off either as an untraceable diversion, or to ceaselessly attack a target before destructing. Hey, maybe even a drone of our own to scout a compound or EMP something, before we go full stealth barsteward or assault the place.
Welding a door shut on another team member notwithstanding (someone played Killing Floor, clearly,) Hardspace: Shipbreaker is a good example of the zero-g mechanics needed for space recovery missions - chop important bits off, guide them towards the ship cargo bay...oops missed, that's a million credits of black box recording floating off into <timcurrry>spaaace</timcurry> ....annnd here come the opposition/pirates, so time to jet back to the ship and evac.
Other on-foot zero-g possibilities like sampling those notable stellar phenomenon could be interesting.
Last thing? Please - no escort missions.