  Let $P(N,V)$ denote the vector space of polynomials of maximal degree less
than or equal to $N$ in $V$ independent variables. This space is preserved by
the enveloping algebra generated by a set of linear, differential operators
representing the Lie algebra $gl(V+1)$. We establish the counterpart of this
property for the vector space $P(M,V) \oplus P(N,V)$ for any values of the
integers $M,N,V$. We show that the operators preserving $P(M,V) \oplus P(N,V)$
generate an abstract superalgebra (non linear if $\Delta=\mid M-N\mid\geq 2$).
A family of algebras is also constructed, extending this particular algebra by
$\Delta -1$ arbitrary complex parameters.
