  Thin-film multiphase superconductors are attracting much attention, and it is
an important issue to propose how to detect them in experiments. In this work,
we study the linear and nonlinear paraconductivity of a bilayer model with
staggered Rashba-type spin-orbit coupling with and without the potential
gradient. This model shows the Bardeen-Cooper-Schrieffer phase,
pair-density-wave phase, and Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phase, and
we focus on how their properties are encoded to the charge transport. We show
that the linear paraconductivity has a peak associated with the phase
transitions between different superconducting states due to the degeneracy of
the transition temperatures as well as the paramagnetic depairing effect. We
also show that the FFLO superconducting state shows a sizable nonlinear
paraconductivity once the degeneracy of Cooper pairs is lifted by applying the
potential gradient. Observation of the peaked linear and nonlinear
paraconductivity can be used as a probe of multiphase superconductivity.
