  The fundamental field equations in modified gravity (including general
relativity; massive and bimetric theories; Ho\vrava-Lifshits, HL;
Einstein--Finsler gravity extensions etc) posses an important decoupling
property with respect to nonholonomic frames with 2 (or 3) +2+2+... spacetime
decompositions. This allows us to construct exact solutions with generic
off--diagonal metrics depending on all spacetime coordinates via generating and
integration functions containing (un-) broken symmetry parameters. Such
nonholonomic configurations/ models have a nice ultraviolet behavior and seem
to be ghost free and (super) renormalizable in a sense of covariant and/or
massive modifications of HL gravity. The apparent noncommutativity and breaking
of Lorentz invariance by quantum effects can be encoded into fibers of
noncommutative tangent Lorentz bundles for corresponding "partner"
anisotropically induced theories. We show how the constructions can be extended
to include conjectured covariant reonormalizable models with massive graviton
fields and effective Einstein fields with (non)commutative variables.
