  We build a supercompact version of the forcing defined in \cite{gitik2019}.
For each singular cardinal in the ground model with any fixed cofinality, which
is a limit of supercompact cardinals, it is possible to force so that the size
of the powerset of the singular cardinal is arbitrarily large, while preserving
the singular cardinal. An important feature of this forcing is that it is
possible to define the forcing so that the successor of the singular cardinal
is collapsed, but all the cardinals above it are preserved.
