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 $-\Delta u+{u}^{3}+\beta u{v}^{2}=\lambda u,-\Delta v+{v}^{3}+\beta {u}^{2}v=\mu v,u,v\in {H}_{0}^{1}\left(\Omega \right),\phantom{\rule{4pt}{0ex}}u,v>0$, 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...