The BHP was made before the advent of +P ammo and most Hi Power experts will not recommend running hotter ammo in a older BHP. While the MARK III cast frame pistols do hold up better for those shooting large amounts of hot-loaded 9mm in either handloaded form or +P, they will wear it out sooner than other modern pistols with hot ammo. Also, it has a weak barrel lug prone to shearing which is why the guns have a 2-piece barrel. It is actually a strengthening measure to use a steel with opposing grain structure from the tube. This is why Bar-Sto aftermarket barrels are also two piece.
ETA: There is no SAAMI spec for +P+ ammo above the already over-loaded +P designation. Since the load is supposed to be still below the pressure of the proof cartridge, it will work if shot rarely in your BHP. But prolonged usage will wear out your gun faster. Because of this fact and the abomination of a trigger linkage on the BHP, I sold my BHP and went to JMB's other design, the 1911 in 9mm. The 1911 in 9mm can handle the hot rod 9mm rounds without accelerated wear. Most 1911 ramped barrels offer plenty of chamber support for hot 9mm loads.