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We present the photometric and spectroscopic evolution of SN 2022oqm, a nearby multipeaked hydrogen- and helium-weak calcium-rich transient (CaRT). SN 2022oqm was detected 13.1 kpc from its host galaxy, the face-on spiral galaxy NGC 5875. Extensive spectroscopic coverage reveals an early hot ( T ≥ 40,000 K) continuum and carbon features observed ∼1 day after discovery, SN Ic-like photospheric-phase spectra, and strong forbidden calcium emission starting 38 days after discovery. SN 2022oqm has a relatively high peak luminosity ( M _B = −17 mag) for CaRTs, making it an outlier in the population. We determine that three power sources are necessary to explain the light curve (LC), with each corresponding to a distinct peak. The first peak is powered by an expanding blackbody with a power-law luminosity, suggesting shock cooling by circumstellar material (CSM). Subsequent LC evolution is powered by a double radioactive decay model, consistent with two sources of photons diffusing through optically thick ejecta. From the LC, we derive an ejecta mass and ^56 Ni mass of ∼0.6 M _⊙ and ∼0.09 M _⊙ . Spectroscopic modeling ∼0.6 M _⊙ of ejecta, and with well-mixed Fe-peak elements throughout. We discuss several physical origins for SN 2022oqm and find either a surprisingly massive white dwarf progenitor or a peculiar stripped envelope model could explain SN 2022oqm. A stripped envelope explosion inside a dense, hydrogen- and helium-poor CSM, akin to SNe Icn, but with a large 56Ni mass and small CSM mass could explain SN 2022oqm. Alternatively, helium detonation on an unexpectedly massive white dwarf could also explain SN 2022oqm.