In this paper we consider the problem of optimally steering an ensemble of battery-powered agents over a network. This is an important problem in applications such as traffic flow control for electric vehicles, where both capacity constraints from the roads and the locations of charging stations need to be taken into account. We extend previous work where origin-destination problems have been formulated using optimal transport. By introducing a state representing the charge level, we can formulate the steering problem as a structured multi-marginal optimal transport problem. The computational method is based on a dual coordinate ascent algorithm applied to the entropy regularized problem, in which we can exploit the decomposable structure of the cost tensor for efficient computations. In this formulation the capacity constraints are represented in terms of certain linear operators, and we derive explicit expressions for the corresponding updates of blocks of the dual variables. Finally, the method is illustrated with a numerical example where vehicles having different charges are required to travel over a grid from origin to destination while minimizing the total energy consumed.