  There are explored off-diagonal deformations of "prime" metrics in Einstein
gravity (for instance, for wormhole configurations) into "target" exact
solutions in f(R,T)-modified and massive/ bi-metric gravity theories. The new
classes of solutions may posses, or not, Killing symmetries and can be
characterized by effective induced masses, anisotropic polarized interactions
and cosmological constants. For nonholonomic deformations with (conformal)
ellipsoid/ toroid and/or solitonic symmetries and, in particular, for small
eccentricity rotoid configurations, we can generate wormholes like objects
matching external black ellipsoid - de Sitter geometries. We conclude that
there are nonholonomic transforms and/or non-trivial limits to exact solutions
in general relativity when modified/ massive gravity effects are modeled by
off-diagonal and/or nonholonomic parametric interactions.
