What model features and calibration strategies yield a large average marginal propensity to consume (MPC) in heterogeneous agent models? Through a systematic investigation of models with different preferences, dimensions of ex-ante heterogeneity, income processes and asset structure, we show that the most important factor is the share and type of hand-to-mouth households. One-asset models either feature a trade-off between a high average MPC and a realistic level of aggregate wealth, or generate an excessively polarized wealth distribution that vastly understates the wealth held by households in the middle of the distribution. Two-asset models that include both liquid and illiquid assets can resolve this tension with a large enough gap between liquid and illiquid returns. We discuss how such return differential can be justified from the perspective of theory and data.