  In a recent letter [\textit{Phys.~Rev.~Lett.}~\textbf{125}, 085001 (2020)],
Dornheim \textit{et al.}~have presented the first \textit{ab initio} path
integral Monte Carlo (PIMC) results for the nonlinear electronic density
response at warm dense matter (WDM) conditions. In the present work, we extend
these considerations by exploring the relation between the nonlinear response
and three-/four-body correlation functions from many-body theory. In
particular, this connection directly implies a comparably increased sensitivity
of the nonlinear response to electronic exchange-correlation (XC) effects,
which is indeed confirmed by our analysis over the entire relevant range of
densities ($r_s=0.5,\dots,10$) and temperatures ($\theta=0.01,\dots,4$).
Finally, our work suggests the possibility of deliberately probing the
nonlinear regime to experimentally probe three- and potentially even four-body
correlation functions in WDM.
