I just read a post by Sandy King, from some years ago... He was joining a few other members' opinion, about HP5+ being a terrible option for pushing... No matter the developer...
Yet Ilford have used the film for long as their flagship product for pushing, from the Microphen era to the DD-X era...
I have pushed it in ID-11, Rodinal, Microphen, DD-X and TMax for more than 20 years.
Sandy says the native low contrast in that film's design, to deal with pushing, makes that film go against a good expansion... HP5+ is a good film for direct sun, not for overcast, they say...