PA+1 can already provide this workflow: Given that nPA proves s and that PA proves all that nPA does, we can get that PA can prove s, and then use the +1 to prove s. And then nnPA can still be handled by PA+1.
PA+1 can already provide this workflow: Given that nPA proves s and that PA proves all that nPA does, we can get that PA can prove s, and then use the +1 to prove s. And then nnPA can still be handled by PA+1.