I'm not sure that the extra matter ever "enters" the black hole in a traditional sense...
As matter approaches it (pass the Schwarzschild radius) and increases in velocity, time slows down more and more for it.
When velocity approaches C, time approaches zero.
Though in another thought, I'd guess that due to the forces involved, the matter is ripped apart on a sub-quantum scale to the point that it literally disintegrates into its energy component and basically adds energy to the black hole (which can be interpreted as mass). But again, it never enters it.
This is a well-understood problem in GR. To an outside observer, things never appear to cross the Schwarzschild radius (R_S), giving the impression that time stops for in-falling matter when it gets to R_S. This, however, is an illusion forced on a distant observer.
The stuff that is actually falling into the black hole never notices R_S because the velocity they measure is not greater than c, and crossing the event horizon is a completely benign event. It's the later extreme tidal forces / spaghettification that destroys in-falling matter.
So it is fair to say that stuff enters a black hole.
As matter approaches it (pass the Schwarzschild radius) and increases in velocity, time slows down more and more for it.
When velocity approaches C, time approaches zero.
Though in another thought, I'd guess that due to the forces involved, the matter is ripped apart on a sub-quantum scale to the point that it literally disintegrates into its energy component and basically adds energy to the black hole (which can be interpreted as mass). But again, it never enters it.