We consider the non-dissipative multi-fluid equations, and demonstrate how multi-Beltrami equilibria emerge as natural relaxed states of the model, representing an evolution towards the minimum energy. General properties of these states are studied, and a wide class of solutions is obtained. We specialize to the cases of double and triple Beltrami states and highlight their connections with the appropriate physical invariants, viz., the generalized helicities and the energy. In particular, we demonstrate that different field configurations can give rise to distinct or identical values of the invariants, depending on the nature of the roots of the multi-Beltrami equation. Moreover, we also highlight equivalences between (outwardly) unconnected models allowing us to treat them in a unified manner. Some observations regarding the nature of the solutions for certain special cases of these models are presented. Potential applications for astrophysical plasmas are also highlighted. © 2015 AIP Publishing LLC.