We reexamine the ${K}^{0}\ensuremath{-}{\overline{K}}^{0}$ system in the ${\mathrm{SU}(2)}_{L}\ifmmode\times\else\texttimes\fi{}{\mathrm{SU}(2)}_{R}\ifmmode\times\else\texttimes\fi{}\mathrm{U}(1)$ model of $\mathrm{CP}$ violation with three generations with special emphasis on the minimal model of spontaneous $\mathrm{CP}$ violation. We give a new estimation of the hadronic matrix elements entering in $\frac{{\ensuremath{\epsilon}}^{\ensuremath{'}}}{\ensuremath{\epsilon}}$, taking into account constraints from current algebra, final-state interactions, and short-distance QCD corrections. We compute, for an arbitrary number of generations, the phenomenological $\mathrm{CP}$ phases in terms of the quark masses, the parameter $r$ (ratio of Higgs vacuum expectation values), and the single $\mathrm{CP}$ phase $\ensuremath{\alpha}$ of the model. We make a three-generation phenomenological analysis taking into account the high multiplicity of the sheets for the $\mathrm{CP}$ phases and the uncertainties in the Kobayashi-Maskawa matrix elements and ${m}_{t}$. For low ${M}_{{W}_{R}}$ the two-generation $\mathrm{LR}$ part dominates for most of the solutions, but the pure $L$ three-generation contribution can be dominant in some cases.