In this article, we examine the dynamics of a multi-fluid system in which (i) different fluids interact, and (ii) there exists a limit in which the multiple fluids evolve into a mixture that satisfies single-fluid approximation. We consider the potential application of this modelling to studies of a cosmological transition which is marked by one material domination replaced by another. The thermodynamical implications of such fluid dynamics are explored where we find that the second law of thermodynamics holds given an emergent Rindler horizon. We argue that such transient periods exist in cosmological evolutions and are best modelled using multi-fluid approximation. Our application of the modelling to an interacting dark-sector leads to the modification of the equation of state of a third non-interacting constituent in a 3-species multi-fluid system.