[smtf]

I've heard a black hole's singularity defined as 'infinitely dense and infinitely small'; I don't think such a thing can be said to 'grow'; however, as the density increases I think that the Event Horizon expands outward increasing the diameter of 'black' so the answer to your question may be yes.

[splat]

Yes. Formally, a singularity is just a "hole" in spacetime. As you increase the mass of the black hole, the singularity itself doesn't change, but the curvature of the spacetime around it becomes stronger.