  We present the most general curvature obstruction to the deformed parabolic
orthosymplectic symmetry subalgebra of the supersymmetric quantum mechanical
models recently developed to describe Lichnerowicz wave operators acting on
arbitrary tensors and spinors. For geometries possessing a
hypersurface-orthogonal homothetic conformal Killing vector we show that the
parabolic subalgebra is enhanced to a (curvature-obstructed) orthosymplectic
algebra. The new symmetries correspond to time-dependent conformal symmetries
of the underlying particle model. We also comment on generalizations germane to
three dimensions and new Chern--Simons-like particle models.
