Yes, Call of Duty: Modern Warfare 3 has full cross-platform support. This means that you can squad up with players on any console  PlayStation, Xbox, or PC  and enter the battlefield together. This is true for any online mode in the game.

Call of Duty: Modern Warfare - Full crossplay between PS4, Xbox One and PC. Also supports cross-progression. Call of Duty: Black Ops Cold War - Full crossplay between PS4, PS5, Xbox One, Xbox Series X/S and PC. Also has cross-progression.