  In this paper, we prove Strichartz estimates for many body Schr\"odinger
equations in the periodic setting, specifically on tori $\mathbb{T}^d$, where
$d\geq 3$. The results hold for both rational and irrational tori, and for
small interacting potentials in a certain sense. Our work is based on the
standard Strichartz estimate for Schr\"odinger operators on periodic domains,
as developed in Bourgain-Demeter \cite{BD}. As a comparison, this result can be
regarded as a periodic analogue of Hong \cite{hong2017strichartz} though we do
not use the same perturbation method. We also note that the perturbation method
fails due to the derivative loss property of the periodic Strichartz estimate.
