This paper addresses the problem of coordinating a large population of heterogeneous electrical loads, such as electric vehicles (EVs) and water heaters (WHs), under global operational constraints. We extend the Moment Constrained Optimal Transport for Control (MCOT-C) framework to accommodate multiple classes of agents with distinct dynamics and cost structures. Our formulation relies on a mean-field limit that captures agent heterogeneity through class-specific distributions. We propose a scalable gradient descent algorithm and a Model Predictive Control (MPC) scheme that enables online adaptation of this algorithm to uncertain or progressively revealed agent information. The proposed approach is validated through numerical experiments on real datasets [8, 9] for EVs and WHs, demonstrating the effectiveness of this method in enforcing global constraints while preserving agent-level dynamics.