According to our current understanding of black holes, if a black hole becomes more massive, it will continue to be a black hole. A black hole is formed when a massive object collapses under its own gravitational force, creating a region in spacetime where gravity is so intense that nothing, not even light, can escape its gravitational pull.
As matter or energy falls into a black hole, its mass and gravitational pull increase. However, the fundamental nature of the black hole does not change. It will always be characterized by its event horizon—the boundary beyond which nothing can escape—and a singularity at its core, where spacetime curvature becomes infinitely strong.
Black holes can grow in mass through accretion, where they capture and consume surrounding matter, or through mergers with other black holes. As they grow, their gravitational pull becomes stronger, but their essential properties as black holes remain the same.
There are theoretical proposals for exotic objects beyond traditional black holes, such as wormholes or hypothetical objects called "black hole alternatives" like gravastars or fuzzballs. These concepts involve speculative ideas and are not yet supported by experimental evidence. Our current understanding, based on general relativity, suggests that sufficiently massive black holes will continue to exist as black holes.