Establishing collective flow in small collision systems is crucial for pinning down the minimum conditions for quark-gluon plasma (QGP) formation. In two-particle correlations, nonflow has been subtracted with good control, pushing the reach of flow measurements down to very small particle multiplicities N. However, the multi-particle nature of collectivity has not been established in the same N regime, because the residual nonflow surviving the subevent procedure in multi-particle cumulants has never been quantified. We develop a general nonflow subtraction framework for m-particle cumulants, built around the approximate 1/Nm−1
Nearby in the stack
scaling of nonflow in the independent-source picture. Correlators containing
v1
serve as clean nonflow estimators, since the
pT
-integrated dipolar flow nearly vanishes. Using as a controlled nonflow-only environment, we test the subtraction for three target observables (
⟨v22⟩
,
⟨v22δpT⟩
, and
c2{4}
) in O+O and
d
+Au at
sNN=5.36
TeV and 200 GeV. Most of the nonflow is removed, with residual fractions typically within 20--30% when converted to the two-particle level, though the best estimator differs across the three targets. We identify a multiplicity-reweighting correction, previously overlooked in two-particle correlations, that explains the long-standing undersubtraction of the naive
1/N
-scaling method; its impact grows as a power of the correlator order. The framework gives a systematic route to nonflow subtraction beyond two-particle correlations, broadening the class of multi-particle observables accessible to the small-system flow program.