If the procedure requires less than 0.3 you need to have special approval (RNP AR APCH being the new term for such approaches AR=approval required) This special approval impacts the operational aspects as much as the airworthiness aspects and in many cases, a formal 'Flight Operational Safety Assessment' has to be carried out - this is done on an operator-by-operator basis.
As I understand it, some Boeing and Airbus models (737, A320..) meet the airworthiness criteria for RNP AR APCH and others are in the approval pipeline but don't expect to fly an RNP 0.15 approach just because that is the lowest figure you can find in the AFM.