<p>This paper investigates the dynamics of a three-oscillator Kuramoto model with higher-order interactions. The higher-order interactions lead to various partial synchronizations of the oscillators. We observe up to nine synchronization transitions as coupling strengths vary and study the phase dynamics near the transition points. Higher-order interactions are more likely to give rise to the uncommon synchronization behavior, also so-called higher-order synchronization. Moreover, the asymmetric higher-order interactions can cause abrupt desynchronization of the oscillators. Under the influence of multiple couplings, coexistence and multistability phenomena induced by high-dimensional bifurcations will occur in the phase plane after the full synchronization of the oscillators.</p>