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In the recent literature, the phenomenon of phase separation for binary mixtures of Bose–Einstein condensates can be understood, from a mathematical point of view, as governed by the asymptotic limit of the stationary Gross–Pitaevskii system $-\Delta u+u^3+\beta u{v}^2=\lambda u,-\Delta v+v^3+\beta u^{2}v=\mu v,u,v\in H_0^1\left(\Omega \right),u,v>0$, as the interspecies scattering length $\beta$ goes to $+\infty$. For this system we consider the associated energy functionals $J_{\beta },\beta \in (0,+\infty )$, with $L^2$-mass constraints, which limit $J_{\infty }$ (as $\beta \to +\infty$) is strongly irregular. For such functionals, we construct multiple critical points via a common...