It has been proposed that one can look for the QCD critical point (CP) by the Beam Energy Scan (BES) accurately monitoring event-by-event fluctuations. This experimental program is under way at the BNL RHIC collider. Separately, it has been studied how clustering of nucleons at freezeout affects proton multiplicity distribution and light nuclei production. It was found that even a minor increase of the range of nuclear forces dramatically increases clustering, while large correlation length $xi$ near CP makes attraction due to binary forces unrealistically large. In this paper we show that repulsive many-body forces near CP should overcome the binary ones and effectively suppress clustering. We also discuss current experimental data and point out locations at which a certain drop in clustering may already be observed.
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