Full concept here.

I'm planning to make a hero shooter, so the game will be mostly or completely multiplayer with the possibility that, like Overwatch, the story will be developed outside the game. But I find that the game needs to have a good backstory in order to immerse players, so it doesn't seem like it's just a bunch of random people fighting each other.

The premise is that the "hero" part of the name takes a new and literal meaning, in that the characters are literal superheroes and supervillains (half the roster the former, the other half the latter). The story and lore of the game is heavily influenced by comic books, as the goal was to create a unique comic book world for the game.

Story

How the story goes is that the setting takes place in an alternate history where superheroes have existed officially since the early 20th century. The most famous superhero is Liberty aka Thomas Williams, a stars-and-stripes wearing super soldier who was commissioned by the United States government to stop the Axis Powers. He fought alongside other heroes in the pursuit to end tyranny. By his side was his best friend, The Crow aka Charles Hall, another super soldier who had known each other since childhood. Together, it was said they were unstoppable. When all was said and done, the Axis Powers were promptly defeated, and a league of superheroes was formed to keep the world safe from threats both within and without. They were known as the Paragon.

The story in present day takes place in the 2020s. The technology is futuristic, similar to what's available in the MCU, as a result of increased scientific development over the decades. The Paragon still stands as the protectors of Earth, and is still led by Liberty, as his aging has been significantly slowed from the super soldier serum. However, things kind of fell apart between the two best friends in the past. The Crow grew to be resentful of Liberty always having the spotlight, of being the leader over him for no apparent reason. The Crow risked as much and worked as hard as him during the war, but received none of the credit. He defected from the Paragon, and formed his own organization called the Dreaded. His powers became corrupted, now rooted in the darkness.

To give himself a place to rule, he took over the unregistered Atlantic islands known as The Haven. With the help of his fellow villains that he recruited, they took over the defenseless place in the course of a night. It now serves as the base of operations for the Dreaded, and the Paragon can't take the fight to them over there, because it's now registered as an official nation by the UN (which would qualify as invasion if they did). The Dreaded have been using their resources and abilities to inflict harm all across the world, but primarily against the Paragon.

Today, there are many heroes and villains who fight for their causes. For centuries there have been secret magic users who guard the world from extraterrestrial threats. People born with psychic abilities have emerged, and there are also those born with superpowers as a result of a genetic mutation. Other cases of people getting superpowers, such as genetic engineering and accidents, have also taken place. The world is very different from what it used to be, that can't be denied.

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How does it look so far? There's a lot more to it than just this, as I've only mentioned two characters and there are multiple factions and layers to the story, but this should give you an idea of what I have in mind. Any feedback and suggestions?

• Liberty is similar enough to Captain America to make you look unoriginal, particularly because the Crow is also very similar not only to Captain America's sidekick Bucky in general, but to the specific variation featured in popular, recent films. Supersoldiers are fine, parody is fine, but in this case you aren't taking Liberty in any new and interesting direction; he's just a copy.
• Political/diplomatic forces opposing military intervention against a "nation" of terrorist supervillains? Only if they have powerful allies, and in that case it's a world war, not a superhero/supervillain issue
  Example scenario: following an horrible act of terrorism, it takes a few phone calls for USA and Russia to contribute equally to a nuclear bombardment with redundant ICBMs. Other powers protest, not for the act but for not having been involved, and the Paragon hunt down Dreaded survivors all around the world.
• The doubtful charisma of a disgruntled ex-hero like the Crow doesn't provide the purpose and leadership a league of supervillains needs. For example, in X-Men comics Magneto and Apocalypse tempt every mutant with their aggressive supremacist political programs. .

• Actually, his powers are different as I've integrated elements of Superman as well. He can fly, shoot lasers, and also possesses a sword. His backstory is different as well, hailing from the rural Midwest area where he was friends with Charles. They grew up together, enlisted in the military together, and both took part in a top secret program to produce super soldiers. As for The Crow, he was never brainwashed like Bucky but became resentful overtime because Liberty got all the rewards and credit just for having a more charismatic personality, eventually becoming his arch nemesis.
• It's a bit more complicated than that. The Haven has a large population of normal people who live under The Crow's reign, and they are essentially the reason why they simply can't just nuke them because it would create a huge moral dilemma. Besides, not just that, but they also have countermeasures for such weaponry even if they tried.
• Once superheroes became a thing, it wasn't much longer until supervillains came into the fray. Someone with power like The Crow is someone they can get behind, it also helps that he actually treats the villains decently (not because of moral reasons, but for pragmatic ones) thus making him charismatic to his followers.

I like what I've read, and the fact that you've said there's more to this through the other characters is encouraging.

For a premise this is fine. But you need to add more depth so that it doesn't look similar to other titles that deal with the same topic. Also, why is this fps?