  We develop the process of symplectic double extensions for Lie superalgebras
with degenerate center. The construction is a superization of a recent work by
Fischer, and generalize our previous work. We provide a standard model for such
double extensions, where the symplectic form is either orthosymplectic or
periplectic. Additionally, we show that every double extension is naturally
equivalent to either of these two standard types of extensions. Several
examples in low dimensions are given to illustrate the concept.
