How to build a corner with two different size cavity walls?
Assemble a 6 1/4" cavity block and two 4 1/4" cavity blocks and place two of the different size blocks up against each other at thief ends. Next set the other 4 1/4" block on top of the block of the same size. Align the larger cavity block by sliding it to a desired position and move the top smaller cavity block to a desired position. Ideally you want the exterior side studs that are exposed internally to be midway in the cavities to provide maximum support for the corner as shown in Diagram 1.

Mark the panels and cut them. Insure that there are three bridges in place in the fist two stud positions from the corner for each cavity wall as shown in Diagram 2.

Use a hook bridge to engage the internal studs that are exposed in the corner and with a zip tie loop the hook bridge and horizontal bridge together level and pull snug as shown in Diagram 3.
Caution: Make sure not to pull too snug, so that you do not pull the corner out of place. Repeat this procedure for the remaining 5 receivers of the studs.

Center the exterior and interior metal corners and attach to the corresponding studs beneath the met al (shorter screws will allow you to remove the metal corner to expose the polystyrene. For additional strength a 1/4" bit of proper length can drill a passage from the interior corner to the exterior corner to allow a 1/4" all thread rod of proper length to be pushed through corresponding holes of each corner as shown in Diagram 4.

On the exterior side a piece of angle iron of desired length with a center hole can be secured with the all -thread rod and proper fasteners for added surface area support. Internally a 1 1/4" dowel about 6" long with a 3/8" hole in the center to act as a washer that can be pivoted to adjust for the varying diagonal angle for different size cavities from the internal to external metal corners as shown in Diagram 5.

You can duplicate this process for each corner of the same size. The only step left is to cut them to size to stagger the vertical seam going up the wall. The builder can use the vertical and horizontal bridges to lock these corners together and with the wall.

Comment: You need to determine how strong the corner needs to be for the size cavities that are being used. You can make these corners exceptionally strong.