  Suppose that the underlying field is of characteristic different from $2, 3$.
In this paper we first prove that the so-called stem deformations of a free
presentations of a finite-dimensional Lie superalgebra $L$ exhaust all the
maximal stem extensions of $L$, up to equivalence of extensions. Then we prove
that multipliers and covers always exist for a Lie superalgebra and they are
unique up to Lie superalgebra isomorphisms. Finally, we describe the
multipliers, covers and maximal stem extensions of Heisenberg superalgebras of
odd centers and model filiform Lie superalgebras.
