  The space of symbols of differential operators on a smooth manifold (i.e.,
the space of symmetric contravariant tensor fields) is naturally a module over
the Lie algebra of vector fields. We study, in the case of $\bf R^n$ with
$n\geq2$, multi-parameter formal deformations of this module. The space of
linear differential operators on $\bf R^n$ provides an important class of such
formal deformations; we show, however, that the whole space of deformations is
much larger.
