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We investigate the microlensing event KMT-2021-BLG-0322, for which the lightcurve exhibits three distinctive sets of caustic-crossing features. It is foundthat the overall features of the light curve are approximately described by abinary-lens (2L1S) model, but the model leaves substantial residuals. We testvarious interpretations with the aim of explaining the residuals. We find thatthe residuals can be explained either by considering a nonrectilinearlens-source motion caused by the microlens-parallax and lens-orbital effects orby adding a low-mass companion to the binary lens (3L1S model). The degeneracybetween the higher-order 2L1S model and the 3L1S model is very severe, makingit difficult to single out a correct solution based on the photometric data.This degeneracy was known before for two previous events (MACHO-97-BLG-41 andOGLE-2013-BLG-0723), which led to the false detections of planets in binarysystems, and thus the identification of the degeneracy for KMT-2021-BLG-0322illustrates that the degeneracy can be not only common but also very severe,emphasizing the need to check both interpretations of deviations from 2L1Smodels. From the Bayesian analysis conducted with the measured lensingobservables of the event timescale, angular Einstein radius, and microlensparallax, it was estimated that the binary lens components have masses $(M_1,M_2) =(0.62^{+0.25}_{-0.26}~M_\odot,0.07^{+0.03}_{-0.03}~M_\odot)$, for both2L1S and 3L1S solutions, and the mass of the tertiary lens component accordingto the 3L1S solution is $M_3=6.40^{+2.64}_{-2.78}~M_{\rm J}$.

KMT-2021-BLG-0322: Severe degeneracy between triple-lens and higher-order binary-lens interpretations