Well the "Modern Military Shooter" tends to imply a certain aim of "authenticity" which is a synonym for "realism".
The problem is the real life is pretty sucky for a video game But i've had a few ideas.
Merge multiplayer, co-op and singleplayer
This is a problem for COD where the type of gameplay in the single-player is jsut far too different from multiplayer.
And example of doing it right would be Team Fortress 2 and Mann vs Machine,
This is also a way to avoid "corridor syndrome" where levels are nothing but a railroaded corridor with zero exploration, just compare a typical COD game to a rail shooter like Time Crisis.
Yet the multiplayer is nothing like this, it's fast, kinetic with so many blind corners and always trying to cover your back. Take a look at this map from an ANCIENT game, Doom, which is 20 years old this year.
Seems complex but that's for single-player, but look at a COD map from multiplayer:
See this genre CAN to intricate, labyrinth and non-linear maps but they are for multiplayer only.
These need to be MERGED, and have the singleplayer campaign consist of "combat zones" where the objective is not simply to get through them to the end but fight in them. And single-player and co-op would have much the same in common, just with co-op the team-mates are player controlled rather than AI controlled. And what you learn in campaign (co-op or single-player) the weapons, items and all that apply equally in competitive multiplayer. So playing the campaign is training for multiplayer.
These areas still have exploration. For example the final level of COD4, the nuclear missile bunker, that should be a labyrinth where you have to explore all over the place to get where you need to go. Not necessarily all done in the same order, you have to actually stop and THINK about where you are and where you need to go. Instead you just had to follow your nose through a load of scripted events.
This is important in terms of game design to really impress on players what environment they are in, they are not in a long winding tube of polygons, they are in (a representation of) a place, where things interact and have significance. It's strange that a game as ancient as Doom is a 3D game that gives me more of a sense of being in a place than most first person shooters today, with their incessant corridor driving forward, you never take a second to look at anything because you're going to pass it and never come back to it.
Create a class and other "pick your own class atributes" inherently unbalances gameplay
In a game like TF2, the fast and small scout doesn't get to chose the health and minigun from the heavy. Trying to have compromise within each perk or from how you don't get another perk doesn't work, you end up having to water everything down so much that perk choices don't mean much.
Have fixed classes and bolt on stuff from there. For example the big huge body builder, he's the guy you can hang a load of armour, ammo and heavy weaponry off, and he won't be slowed down as much. The guy with the steady hand is not going to be a high strung guy, the sniper is going to be physically fit but not or sprinting or fighting, he can be accurate with a sniper rifle at the cost of slugging ability.
body armour is the asnwer to OP weapons
Real if weapons are very deadly, fully automatic, powerful and accurate it takes all the gameplay out of the game as you just have to click on them and they are dead, it's beyond even reaction time, it's simply whoever saw the other first. But body armour can iron this out, at the cost of a bit of speed and how much you can carry.
few weapons balance ideas
Pistols are inherently going to be weak and held back by a low fire rate, balance this by how you can effectively have them constantly sighted in when the weapon is drawn. Actually holding the "use sights" button only moves the lined up sights towards the centre of the screen.
To balance out pistols, most rifles are semi-auto or burst. Because this IS how they are actually used, the full auto is for extreme close quarters and suppressive fire
soldiers in modern armies are trained to aim and fire single shots to kill specific targets not pin the trigger and mag-dump. Now assault rifles are "controllable" in full auto, but they are not accurate. The gun won't fly up in the air, it will stay controllabel enough to spray an area, but anything beyond very close range you will put more shots on target in 10 seconds with rapid single-shot fire than with held-down full auto.
There are 2 ways to get effective "full auto":
-Submachine guns: these are weaker and about as heavy as assault rifles, the weaker round won't have as much recoil. These will have higher dps in terms of shots hitting over medium distance. They are essentially identical in handling to assault rifles (who quickly they can be hefted around) but pinning the trigger works. COD seems to be going the opposite way strangely, they are making the submachine-guns more powerful and less controllable, while the assault rifles are weaker and more controllable.
-Belt-fed Machine guns: these have identical ballistics and damage as assault rifles, but by being a heavier weapon they can absorb the recoil for controllable full auto fire at the cost of extremely limited handling and mobility.
-make headshots worth it: these measly 1.4x headshot multiplier hardly matter. It's their freaking cranium, don't tell me by brain is only 40% more vulnerable than my shin.