We develop a dynamic model of a multi-asset over-the-counter (OTC) market that operates via search and bargaining and empirically test its implications regarding liquidity in the cross section of assets. The key novelty in our model is that investors can hold and manage portfolios of OTC-traded assets. We characterize the stationary equilibrium in closed form and derive natural proxies for asset-specific measures of market liquidity including trade volume, price dispersion, and price impact. Our theoretical results uncover how the general equilibrium (GE) effects shape the patterns of liquidity measures in the cross section of OTC-traded assets. For example, heightened search frictions in one asset trigger fire sales in other assets by increasing other assets' trade volume but also making them trade with larger price impact and price dispersion. Based on data from the US corporate bond market and the credit default swap (CDS) market, our empirical tests confirm these key cross-sectional liquidity implications of our general-equilibrium OTC framework.