RNP value should change by itself as the aircraft moves to differant phases of the approach (0.3 for the final approach seg of an RNAV App). There is however nothing stopping you from changing this during your App Prep. I has seen cases where the RNP did not auto-adjust. This could be a Database coding error and should be taken up with your Database provider (Honeywell, Smiths, Jepp ect).
If you have changed the required RNP to the most restrictive value and you get a Nav Accuracy Downgrade Caution it might not prevent you from continuing that phase of the approach which might have required a less restrictive value (ie 0.5nm for an initial app seg).
PS. I am a Airbus driver so the Boeing (or other) info might be different.