Multiphase flows are ubiquitous in natural and engineering systems and are characterized by strong nonlinearity, multiscale coupling, and sharp interfacial dynamics. Conventional partial differential equation (PDE)–based solvers provide accurate descriptions but remain computationally prohibitive for large-scale or real-time spatiotemporal prediction. Recent data-driven approaches, such as neural operators and latent-space reduced-order models, have shown promise, yet their application to multiphase flows is still limited by insufficient nonlinear expressiveness, poor robustness to noise, and weak generalization across different phase configurations. To address these challenges, we propose MultiOKAN, a composite latent-space operator learning framework that integrates a Kolmogorov–Arnold Network–based autoencoder (KAE) with a KAN-enhanced Deep Operator Network (DeepOKAN). The KAE compresses high-dimensional phase volume-fraction fields into compact latent representations that preserve essential interfacial features, while DeepOKAN learns the nonlinear temporal operator that maps initial latent states directly to future evolution. This design enables efficient, end-to-end prediction of multiphase spatiotemporal dynamics without explicit PDE solvers. Notably, this study presents the first systematic validation of the deep learning architecture across a broad spectrum of multiphase scenarios (including bubble rise, particle deposition, and fluidized bed two-phase flows, as well as a coupled three-phase system). It demonstrates its excellent efficiency and accuracy in accelerated computation and spatiotemporal evolution prediction, while exhibiting strong robustness under noisy training conditions. Further analyses reveal its data efficiency and clarify the effects of training-set size and temporal resolution on predictive accuracy. Extension studies confirm the scalability of the framework to higher-order multiphase systems. Overall, MultiOKAN provides an efficient and robust neural-operator-based pathway for real-time spatiotemporal prediction of complex multiphase flows, with significant potential for scientific modeling and engineering applications.