Camera Calibration - Chaining Transformations


I am trying to calibrate a multi-camera system. Currently I can accurately calibrate intrinsic and extrinsic parameters achieving a reprojection error of about 0.2 pixels.

However, I want to try a new layout (Currently using an arc style layout) and I’m not sure how difficult it will be to calibrate the cameras that are opposite to one another (1 and 3 or 2 and 4 seen in the picture for example).
If I select camera 1 as my world origin camera and try to do a direct calibration between 1 and 3 where I capture chessboard images I think it will be difficult to get good calibration images since the cameras are essentially facing one another.

Has anyone had any experience calibrating two cameras that are essentially opposite/facing one another?
Would it be better to calibrate 1, 2, and 4 together and then calibrate camera 3 later and chain the transformations together in such a way that I can obtain the transform from camera 1 to 3?