  We generalize the formulation of Poisson-Lie (PL) T-plurality proposed by R.
von Unge [JHEP 07 (2002) 014] from Lie groups to Lie supergroups. By taking a
convenient ansatz for metric of the $\sigma$-model in terms of the
left-invariant one-forms of the isometry Lie supergroups $(C^3 +A)$ and
$GL(1|1)$ we construct cosmological string backgrounds, including
$(2+1|2)$-dimensional metric, time-dependent dilaton and vanishing torsion, in
a way that they satisfy the one-loop beta-function equations. Starting from the
decompositions of semi-Abelian Drinfeld superdoubles (DSDs) generated by the
$({\C}^3 +{\A})$ and $gl(1|1)$ Lie super bi-algebras we find the conformal
duality/plurality chains of $2+1$-dimensional cosmological string backgrounds
coupling with two fermionic fields. In particular, the new backgrounds obtained
by the super PL T-plurality remain conformally invariant at one-loop level.
This work can prompt many new insights into supergravity and obviously has
interesting mathematical relations with double field theory.
