A biotic battle-staff that can separate into an omni-sword/shield, and vice-versa.
Battle-staff for ranged attacks (Vanguard Pull/Shockwave or Sentinel Throw/Warp)
Omni-sword/shield for melee
(Yes, I know that sounds a lot like Dragon Age)
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If it must be straight-up guns, then I would want something that is completely modular, akin to the B.L.A.D.E. from "VANQUISH"
The idea is that I only need to bring ONE weapon and it acts as a pistol in it's default form.
So I add a rotating magazine and a mid-sized barrel, and BAM, assault rifle.
Switch it out with a heavy stock and a larger thermal clip, and BAM, shotgun.
Change to a long-barrel and a scope, and BAM, sniper rifle.
For gameplay balance it could be that I can change it to whatever I want, whenever I want, but the heat generated with each transition uses up thermal clips.
Or that I have to pick the mods I want for each weapon "style" before the mission and I have to stick with those the whole way through.
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Perhaps a "Secondary Fire" feature.
I could have a Shotgun that deploys a full-cover omni-shield around the gun (a bit like the Typhoon) so I can pull a "Clear and Hold" strategy while advancing at a steady pace.
Or an Assault Rifle that has a micro-missile-defense system, except it "shoots down" enemy grenades. It would allow suppressing fire without having to worry about being flushed out.
What about a Sniper Rifle that has a mass-accelerator "pellet-gun" on the under-barrel that acts as a deterrent against any enemy that tries to get into melee range? It would allow the sniper to focus more on taking the shot rather than worrying about being flanked.
For balance, the shield could be forward-facing only, so it's possible to get flanked. The micro-defense system could have a limited rate of fire. The under-barrel pellet gun could have knockback, but negligible damage.
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A bit meta, but I'd like the ability to change your class within the game. It wouldn't be free, and it wouldn't be something lightly done either, but considering YOU are the best weapon in the game, it would greatly add to your power and capability to be able to switch your proficiency/ability set by choice instead of being "locked" into one particular class.
Soldier -> Vanguard : 1000 eezo, 20 weapon components, 5 ammo converters, 5000 credits
Soldier -> Adept : 2500 eezo, 5 weapon components, 1 ammo converter, 10000 credits
Vanguard -> Sentinel : 500 eezo, 1 omni-tool processor, 1 ablative armor chassis, 7500 credits
Vanguard -> Engineer : 1000 eezo, 2 omni-tool processor, 1 drone construct, 10000 credits
Not a perfect representation, but the idea is that the farther you go from your current class, the more expensive it becomes. Even going to a "neighboring class" wouldn't be cheap, so you would have to really consider the cost of doing so.
SHORT VERSION: I want my Vanguard/Sentinel hybrid!