>Objects more massive than [2 to 3 times the mass of the Sun] can only be black holes

One (pedantic) correction: objects more massive cannot be held up by neutron degeneracy pressure, but you can have more massive stars held up by radiation pressure from fusion. Certainly, there are many giant stars in the 2-8 solar mass range, and rarer stars in tens-to-hundreds of solar masses. Of course, they will eventually burn away their fusion fuel, and the core remnant may indeed become a black hole.