  We discuss a general framework for cutting constructions and reinterpret in
this setting the work on non-Abelian symplectic cuts by Weitsman. We then
introduce two analogous non-Abelian modification constructions for
hyperk\"ahler manifolds: one modifies the topology significantly, the other
gives metric deformations. We highlight ways in which the geometry of moment
maps for non-Abelian hyperk\"ahler actions differs from the Abelian case and
from the non-Abelian symplectic case.
