Suppose you are organizing a reading group and must allocate 10 discussion topics and 10 dates to 10 students. Students may have combinatorial preferences over (topic, date) bundles—their preferences over one component may depend on the other component. How would you design the mechanism to allocate the topics and dates?

We focus on two classical settings in multi-type resource allocation. For resource allocation without initial endowments, we characterize serial dictatorships by a minimal set of three properties: strategy-proofness, non-bossiness, and category-wise neutrality. For resource allocation with initial endowments, we show that the Top-Trading-Cycles mechanism can be naturally extended while preserving most of its desirable properties, when agents’ preferences are lexicographic.