I friend told me this can be done, I wouldn't mind teaming up with friends in Federation if it's true. I tried looking for it online but I didn't see any info on this.
No, the game is hard coded with blue (fed) and red (kdf) factions and currently teaming between those factions or a third neutral faction aren't possible. Even Romulan and Jemhadar have pick an ally to use most systems in the game.
Just make it 100% sure fed and kdf pick their faction at character creation and it cannot be changed after that, there z-store race option for fed allied klingon but those are fed characters from creation, not character who swapped factions after creation.
The only time a KDF can team with a Fed is during TFOs. Other than that, as mentioned above, STO still follows the ancient two faction system of MMOs, and KDF is the Red Faction. Other than TFOs, Red and Blue do not mix. Cryptic has brought down many walls, but the Red/Blue Faction Wall is base code foundation deep, like "we might as well make a new game" deep.
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