4th independent AXIS

Sadly Klipper doesn’t allow to move the A axis synchronously with the cartesian axes (eg. G1 A100 X50 E10), . The planner only support XYZE axes.
Some people have been working on this, but it requires in depth modification that will probably never be integrated in mainline Klipper. See:

It’s possible to sequence manual stepper moves to run in parallel with planned cartesian moves (using SYNC=0). But you’ll have to infer what the planner is doing with the cartesian axes to provide the correct ACCEL and SPEED to keep the A axis in sync. This can get complicated, with lots of edge cases.

On the other hand if the movements of the additional axis are only to be sequenced in between cartesian moves, you can write a macro overloading the G0/G1 commands to dispatch the coordinates to MANUAL_STEPPER when A is used, or the original G0 otherwise.