If however you wanted to run the X and Y while A was at rest (loading parts?), then run X and A while unloading/loading Y, I think you would be fine.
Just set up A as another linear axis and adjust the Gcode accordingly.
Just looked at one of these machines,(gougle) how is it originally intended to work with 2 tables ?
Looks like 1 common X and spindle with 2 (y,a)tables. ? ? What a beast !
Just guessing,
Russ