  We present a study on the many-body exciton interactions in a prototype
Ruddlesden-Popper metal halide (RPMH), namely \ce{(PEA)2SnI4} (PEA =
phenylethylammine), using coherent two-dimensional electronic spectroscopy. The
optical dephasing times of the third-order polarization observed in these
systems are determined by exciton many-body interactions and lattice
fluctuations. We investigate the excitation-induced dephasing (EID) and observe
a significant reduction of the contribution to the dephasing time with
increasing excitation density as compared to its lead counterpart
\ce{(PEA)2PbI4}, which we have previously reported
[A.~R.~Srimath~Kandada~\textit{et~al.}, J.\ Chem.\ Phys.\ \textbf{153}, 164706
(2020)]. Surprisingly, we find that the EID interaction parameter is four
orders of magnitude higher in \ce{(PEA)2SnI4} than that in \ce{(PEA)2PbI4}.
This increase in the EID rate may be due to exciton localization arising from a
more strongly statically disordered lattice in the tin derivative. This is
supported by the observation of multiple closely spaced exciton states and the
broadening of the linewidth with increasing population time (spectral
diffusion), which suggests a static disordered structure relative to the highly
dynamic lead-halide. Additionally, we find that the exciton nonlinear coherent
lineshape shows evidence of a biexcitonic state with low binding energy
($<10$\,meV) not observed in the lead system. We model the lineshapes based on
a stochastic scattering theory that accounts for the interaction with a
non-stationary population of dark background excitations. Our study provides
evidence of differences in the exciton quantum dynamics between tin- and
lead-based RPMHs and links them to the exciton-exciton interaction strength and
the static disorder aspect of the crystalline structure.
