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Microlasers in near-degenerate supermodes lay the cornerstone for studies of non-Hermitian physics, novel light sources, and advanced sensors. Recent experiments of the stimulated scattering in supermode microcavities reported beating phenomena, interpreted as dual-mode lasing, which, however, contradicts their single-mode nature due to the clamped pump field. Here, we investigate the supermode Raman laser in a whispering-gallery microcavity and demonstrate experimentally its single-mode lasing behavior with a side-mode suppression ratio (SMSR) up to 37 dB, despite the emergence of near-degenerate supermodes by the backscattering between counterpropagating waves. Moreover, the beating signal is recognized as the transient interference during the switching process between the two supermode lasers. Self-injection is exploited to manipulate the lasing supermodes, where the SMSR is further improved by 15 dB and the laser linewidth is below 100 Hz. [ABSTRACT FROM AUTHOR]