We consider a model with two competing two-sided platforms that sell directly to one side of the market (the "direct side"), and indirectly through an agent to the other side (the "retail side"). The platforms offer non-linear tariffs to the agent, and they are allowed to endogenously choose whether to contract with the same or different agents. In this setting we study the platforms' incentives to impose minimum or maximum RPM, and the effect on the final market outcome. We find that, even if customers on both sides value each other's participation, the firms may want to impose minimum RPM on the agent if the competition between the platforms is sufficiently strong, in order to raise prices on both sides of the market simultaneously. In a linear demand example we show that RPM reduces overall welfare when the equilibrium involves the use of minimum prices, and increases welfare when the equilibrium involves maximum prices.