Multi-modal multi-task (M3T) foundation models (FMs) have recently shown transformative potential in artificial intelligence, with emerging applications in education. However, their deployment in real-world educational settings is hindered by privacy regulations, data silos, and limited domain-specific data availability. We introduce M3T Federated Foundation Models (FedFMs) for education: a paradigm that integrates federated learning (FL) with M3T FMs to enable collaborative, privacy-preserving training across decentralized institutions while accommodating diverse modalities and tasks. Subsequently, this position paper aims to unveil M3T FedFMs as a promising yet underexplored approach to the education community, explore its potentials, and reveal its related future research directions. We outline how M3T FedFMs can advance three critical pillars of next-generation intelligent education systems: (i) privacy preservation, by keeping sensitive multi-modal student and institutional data local; (ii) personalization, through modular architectures enabling tailored models for students, instructors, and institutions; and (iii) equity and inclusivity, by facilitating participation from underrepresented and resource-constrained entities. We finally identify various open research challenges, including studying of (i) inter-institution heterogeneous privacy regulations, (ii) the non-uniformity of data modalities' characteristics, (iii) the unlearning approaches for M3T FedFMs, (iv) the continual learning frameworks for M3T FedFMs, and (v) M3T FedFM model interpretability, which must be collectively addressed for practical deployment.