  We introduce a simple deformed quantization prescription that interpolates
the classical and quantum sectors of Weinberg's nonlinear quantum theory. The
result is a novel classical limit where $\hbar$ is kept fixed while a
dimensionless mesoscopic parameter, $\lambda\in[0,1]$, goes to zero. Unlike the
standard classical limit, which holds good up to a certain timescale, ours is a
precise limit incorporating true dynamical chaos, no dispersion, an absence of
macroscopic superpositions and a complete recovery of the symplectic geometry
of classical phase space. We develop the formalism, and discover that energy
levels suffer a {\em generic perturbation\/}. Exactly, they become
$E(\lambda^{2}\hbar)$, where $\lambda = 1$ gives the standard prediction. Exact
interpolative eigenstates can be similarly constructed. Unlike the linear case,
these need no longer be orthogonal. A formal solution for the interpolative
dynamics is given, and we exhibit the free particle as one exactly soluble
case. Dispersion is reduced, to vanish at $\lambda = 0$. We conclude by
discussing some possible empirical signatures, and explore the obstructions to
a satisfactory physical interpretation.
