Let $\Delta$ be a simplicial complex on $V = \{x_1,...,x_n\}$, with
Stanley-Reisner ideal $I_{\Delta}\subseteq R = k[x_1,...,x_n]$. The goal of
this paper is to investigate the class of artinian algebras
$A=A(\Delta,a_1,...,a_n)= R/(I_{\Delta},x_1^{a_1},...,x_n^{a_n})$, where each
$a_i \geq 2$. By utilizing the technique of Macaulay's inverse systems, we can
explicitly describe the socle of $A$ in terms of $\Delta$. As a consequence, we
determine the simplicial complexes, that we will call {\em levelable}, for
which there exists a tuple $(a_1,...,a_n)$ such that $A(\Delta,a_1,...,a_n)$ is
a level algebra.