Had some extra ideas on my mind so i felt like adding em in.

TDM- Of course everyone knows about this or suggests it so theirs no point in going on.

FootBall
Ok exactly how it sounds but instead have a bomb in the middle of the map. Teams rush it to the enemies base in order to arm it and blow up their base. (Ofc) Bombs time will be armed for a max of 30 seconds. Engineers needed to disarm. Ops needed to track enemies and ball carrier. Engineers need to defend. And Medics just do their thang.

Search and Destroy
Double health, no respawns unless medic revives you.

Captain
Basically one lucky player is deemed the fat man on a escort mission to a certain objective. Captain will move slow and have a reasonable amount of hp. Buffs are as they are now. Heals will be reduced to 1/2. The fatman has a gatling gun and CAN shoot back, but has poor acc and cannot sprint.

Escape
Team A is on the run from Team B. Team A has only has a riot shield while Team B has the oppurtinity to try and gun them down. Team A has to successfully get to the objective. For every successful escape, points are rewarded to the team. Team with most points wins. Teams switch over after every match.

Capture the bag/flag
As it says it is.

My ideas for game modes. (Tweaking may be needed)

No TDM.

Go to competition mode instead.

Football? How about a simple CTF? Chasing a guy is troublesome lol.

Search and Destroy? Get back to CoD. Objective based, no camping...

Captain? We have escort missions. No need to design the MVP as a player.

I gave up on reading your modes. No offense but I'm fine with the maps. It's the team that makes it great.

Dont reply if you dont read the whole thing cuz it seems like your lost.

Ive seen football in action on other shooter games, pretty popular. Work to get the bomb to the enemy base and detonate it.
Search and destroy....Hmmm i just said that randomly because it may work with a bit of tweaking.
Captain, Yes escort missions with bots. But this gets players more involved.