A quasi-star is a hypothetical supermassive star that is so heavy its core collapses into a black hole as it is still forming. The matter accreting into the black hole then generates radiation pressure that keeps the star from imploding.
These are supposed to be extremely massive stars of 1000 or more M☉, but the most massive regular star is about 250 M☉.
There is a gap there, as well as a precedent in the form of Thorne–Żytkow objects, which are stars with a neutron star at their core due to a collision. The neutron star will feed on its host until the entire host star is consumed or it collapses into a black hole and the host star falls in, whichever comes first.
Based on this, a supermassive star with a neutron star at its core, formed the same way as a quasi-star but with less mass involved, looks plausible, but I don't know enough about the physics involved to tell for sure.
Is this realistic, and if not, what does happen to a 500 or 750 M☉ star as it is forming?