We conduct a systematic analysis of heterogeneous agent consumption-saving models to understand whether and how they can generate a large average marginal propensity to consume (MPC). One-asset models without ex-ante heterogeneity feature a trade-off between a high average MPC and a realistic level of aggregate wealth. One-asset models with additional heterogeneity in preferences or rates of return, or behavioral features, can generate high MPCs with the right amount of total wealth, but at the cost of an excessively polarized wealth distribution that understates the wealth held by households in the middle of the distribution. Two-asset models that include both liquid and illiquid assets can resolve these trade-offs without ex-ante heterogeneity or behavioral elements, although these additional features can improve the fit of the model in other dimensions. Across all models, the share and type of hand-to-mouth households is the most important factor that determines the level of the average MPC.