The basic principle of TCAS is once the RA is issued never try anything against it by going visual. It's dangerous because you can't think for both.
Boeing SOP is that PM should be looking for the conflicting traffic, and then to "
maneuver if needed". I'm not a fan of this advice and tend to think that PM's attention would be better spent monitoring PF, especially since the Boeing philosophy of disconnecting the autothrottle increases the PF's workload in addition to the RA startle factor.