  In recent years the femtoscopy technique has been used by the ALICE
Collaboration in small colliding systems at the LHC to investigate the
strong-interaction of hadron pairs in the low-energy regime. The extension of
this technique to the study of many-body correlations aims to deliver in the
next years the first experimental measurements of the genuine many-hadron
interactions, provided that the contributions due to the lower order terms are
properly accounted for. In this paper we present a method that allows to
determine the residual lower order contributions to the three-body correlation
functions, based on the cumulant decomposition approach and on kinematic
transformations. A procedure to simulate genuine three-body correlations in
three-baryon correlation functions is also developed. A qualitative study of
the produced correlation signal is performed by varying the strength of the
adopted three-body interaction model and comparisons with the expectations for
the lower order contributions to the correlation function are shown. The method
can be also applied to evaluate the combinatorial background in the two-body
correlation functions, providing an improved statistical accuracy with respect
to the standard techniques. The example of the contribution by the pK$^+$K$^-$
channel to the recently measured p$\phi$ correlation is discussed.
