This paper studies multi-object reallocation without monetary transfers, where agents initially own multiple indivisible objects and have strict preferences over bundles (e.g., shift exchange among workers at a firm). We focus first on marginal rules, which elicit only rankings over individual objects, and characterize the generalized Top Trading Cycles rule (TTC) on the lexicographic and responsive domains. On the lexicographic domain, TTC is the unique balanced rule satisfying Pareto efficiency, the worst-endowment lower bound, and either truncation-proofness or drop strategy-proofness. On the responsive domain, TTC is the unique marginal rule satisfying individual-good efficiency, truncation-proofness, and either the worst-endowment lower bound or individual rationality. In the Shapley–Scarf housing market, TTC is characterized by Pareto efficiency, individual rationality, and truncation-proofness. We also consider conditionally lexicographic preferences, which admit complementarities and are represented by lexicographic preference trees. On this domain, the augmented Top Trading Cycles rule (ATTC) is the unique balanced rule satisfying Pareto efficiency, the worst-endowment lower bound, and drop strategy-proofness. The conditionally lexicographic preferences are a maximal domain for the equivalence between Pareto efficiency and individual-good efficiency, and also for the compatibility of balancedness, Pareto efficiency, and individual rationality.