A growing number of platforms including those run by Amazon, Apple, Google and Microsoft operate in a dual mode: running marketplaces for third-party products, while also selling their own products on those marketplaces. We build a model to explore the implications of this controversial practice, taking into account the endogeneity of third-party sellers' innovation decisions. We analyze the tradeoffs that arise from a ban on the dual mode, showing how such a ban can harm consumer surplus and welfare even when the platform would otherwise engage in product imitation and self-preferencing. Instead, in the empirically most relevant scenarios, policies that prevent platform imitation and self-preferencing lead to better outcomes than an outright ban on the dual mode.