We provide a canonical and tractable model of a trading platform which controls the product variety it hosts and product prices by charging a percentage fee on sellers and choosing whether to sell its own product (hybrid mode). We micro-found and derive a mixed market demand system for differentiated products to capture interactions between monopolistically competitive sellers and a sizeable range of platform products. The hybrid platform steers consumers towards its products by charging higher seller fees than pure marketplace. This ``insidious steering" intensifies the better the platform's own products. Banning hybrid mode benefits consumers if and only if the ban leads to pure marketplace. The hybrid platform debases third-party products if its products are strong enough. We capture two-sided network effects by endogenizing buyer participation via costs to discover tastes for products and seller participation via an aggregate manipulated by the platform's fee.