The 744 can do RNP and P-RNAV. The only thing it MAY not be able to do is RNP 0.3 approaches.
This is interesting and confusing to me (highlighted in my bold). Approach RNP 0.3 is a basic level of containment to be RNP capable.
Do you mean <0.3 RNP approaches?
...there are problems with some approaches with tight turns
Or do you mean containment issues on RF turns during 0.3 RNP approaches?
It may be a matter of company certification (OpSpec C384?), but we are certified to RNP1. We cannot do the RNAV approaches marked as "RNP 0.3" or "RNP 0.1" ("RNP SAAAR") in the 400. That's why I emphasized "MAY not"...
Example of the turn problem is the ILS DME-1 Rwy 23L into MMMX. The FMS will not make that last turn to final without significant overshoot, unless we manually intervene. I haven't flown it in the -8, but it's the topic of much company discussion.