Harmful social norms often persist despite legal and economic sanctions against them. Can the abandonment of a harmful norm be facilitated by the presence of a 'mildly harmful' alternative that may act as a stepping stone in the medium run? Or will this become a new absorbing norm? We propose a dynamic, game-theoretic model to analyze this question, focusing on interim dynamics. We derive necessary and sufficient conditions for a stepping stone transition, which involve as key parameters the social penalty factors and the difference in intrinsic utilities of the various actions. We explore the implications of the model using original data on female genital cutting in Somalia, where a transition is underway from an extremely invasive to a milder form of cutting. The framework is general and can be applied to other examples, both contemporary and historical, including footbinding, dueling, child marriage and smoking. Our analysis underlines the importance of considering intermediate alternatives when formulating policies against harmful norms.