I think at first step, test this patient's cells use anti-AB, if the reaction is stronger than with anti-A, then it is Ax type.
2nd, if the anti-AB reaction strength is the same with anti-A, then do adsorption and elution test, to see if there are A antigens on the cells.
3nd, test the cells use anti-H, to see if there is some kind of parabombay or more rarely bombay type.
As to the reverse group, I think we should add a tube of O cells as negtive control, to make sure the reaction when we add more serum or prolong the incubation time or incubation them at 4 degree C is actually anti-A.
This is my personally opinions