If the system is ericsson there are two parameters that you can play with:
1-OFFSET: by changing this parameter you are moving the border inside one of the cells.
in your case you want to maintain the call in cell A so you increase the parameter OFFSETP in the cell realation CELLA_CELLB (note that the parameter OFFSETN will be increased automatically by the same value in the oppisite direction CELLB_CELLA).
2-for the bingbong handover you have three parameter (HIHYST, LOHIST and HYSTSEP)the HYSTSEP parameters indicated where the handover is happenning (in your case its in 70s to 80s dbm) so if HYSTSEP is still in its deafault value which is 90 , the handover is happening in a high Signal Streangh so you change the HIHYST ( increase it to deteriorate the pingpong handover ).
hope you find this useful,