I agree with 777fly - there isn't anything that Boeing recommends.
From the Non Normal Checklist introduction (also in the FCTM)
"It should be noted that, in determining the safest course of action, troubleshooting, i.e. taking steps beyond published non-normal checklist steps, may cause further loss of system function or system failure. Troubleshooting should only be considered when completion of the published non-normal checklist results in an unacceptable situation"
There was a reference regarding not using synoptic displays as a basis for doing a non normal checklist, but I can't find it at the moment.
So for me, I'd be sitting on my hands and monitoring.