The exceptional combination of strength and ductility in multi-component alloys is often attributed to the interaction of dislocations with the various solute atoms in the alloy. To study these effects on the mechanical properties of such alloys there is a need to develop a modeling framework capable of quantifying the effect of these solutes on the evolution of dislocation networks. Large scale three-dimensional (3D) Discrete dislocation dynamics (DDD) simulations can provide access to such studies but to date no relevant approaches are available that aim for a complete representation of real alloys with arbitrary chemical compositions. Here, we introduce a formulation of dislocation interaction with substitutional solute atoms in fcc alloys in 3D DDD simulations that accounts for solute strengthening induced by atomic misfit as well as fluctuations in the cross-slip activation energy. Using this model, we show that local fluctuations in the chemical composition of various CrFeCoNi-based multi-principal element alloys (MPEA) lead to sluggish dislocation motion, frequent cross-slip and alignment of dislocations with solute aggregation features, explaining experimental observations related to mechanical behavior and dislocation activity. The developed method also provides a basis for further investigations of dislocation plasticity in any real arbitrary fcc alloy with substitutional solutes.