We prove that at least half of the first-best gains from trade can always be achieved in multidimensional two-sided markets with additive values and costs and arbitrary downward-closed feasibility constraints. The guarantee is achieved by a mechanism satisfying Bayesian incentive compatibility, interim individual rationality, and strong budget balance, and is tight already in single-item bilateral trade. Types are independent across agents, while the coordinates of each agent's type may be arbitrarily correlated. Feasibility constraints may couple trades across items and agents. This extends the known tight one-half guarantee for single-item bilateral trade. Our proof develops a new application of the Cai--Devanur--Weinberg duality framework. We show that the objective of every feasible dual is at least half of the first best. Strong duality then yields the guarantee without characterizing an optimal mechanism or dual. The key observation is that every feasible dual induces continuous-time Markov chains that, when stopped by exponential clocks, recover true types as expectations of virtual types. The dual constraints control the rate at which these chains change the prior distributions. We establish our bound by combining this control with a coupling of the agents' clocks.

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