Dominant online platforms are increasingly collecting user-specific data across multiple markets, raising red flags as regards privacy, as well as potential anti-competitive abuses. We analyze competition among two platforms, with one platform collecting data in market 1 where it is dominant, using it to improve its competitive edge in market 2 where it competes in both prices and advertisements with the other platform. Our analysis unearths a novel anti-competitive effect of competition—that increased market 2 competition may increase the dominant firm’s market power in market 1, which in turn leads to several interesting results. First, that data collection by the dominant firm is increasing in market 2 competition. Second, efficiency of data collection is non-monotonic in the level of competition; being, from a welfare perspective, excessive (respectively low) whenever market competition is at an intermediate level (respectively weak). We then use this framework to examine several policy proposals—user control of data, blocking data-driven mergers, restricting data collection, and allowing data-sharing—deriving actionable prescriptions for managers and policymakers. For example, in markets with effective ad-targeting, we find that user control of data decreases data collection, thus improving privacy, if and only if competition is strong.