A general model for the dissolution of stoichiometric particles in multi-component alloys is proposed and analysed. We introduce the concept of mass-conserving solutions and give a self-similar solution for the resulting Stefan-problem. Furthermore, we show that particle dissolution in multi-component alloys can under certain circumstances be approximated by a model for particle dissolution in binary alloys. Subsequently, we propose a numerical method to solve the coupled dissolution problem. We end with some examples of hypothetical applications from metallurgy.