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If you calibrate you cameras with the same chessboard, without moving it for all cameras, they are already in the same coordinate systems.

Each extrinsic parameters gives you the Rotation and Translation from the origin (aka the first inner corner of the chessboard) to the camera. Therefore, if the chessboard isn't moving during the extrinsic calibration process, each calibration results are in the same coordinate systems.

Is it what you want?