Can one theoretically increase the spin of a black hole by adding mass at the right angle? IE: give it more and more angular momentum until you achieve the naked singularity?
Perhaps that is the final experiment of Kardashev level whatever civilization.
You absolutely could keep adding momenting in just the right way. Though I will add, as spin goes up, so does frame dragging, which makes it actually difficult to hit a black hole as space begins spinning with it.
It makes for a very nice sci-fi story setting though. A very far flung future in which some very post-humans are attempting to break the universe in this way.
Perhaps that is the final experiment of Kardashev level whatever civilization.