  The so-called $\chi^{2}$-superstatistics of Beck and Cohen (BC) is employed
to investigate the infinite-range Blume-Capel model, a well-known
representative system displaying inequivalence of canonical and microcanonical
phase diagrams. While not being restricted to any of those particular
thermodynamic limits, our analytical result can smoothly recover both canonical
and microcanonical ensemble solutions as its nonextensive parameter $q$ is
properly tuned. Additionally, we compare our findings to ones previously
obtained from a generalized canonical framework named Extended Gaussian
ensemble (EGE). Finally, we show that both EGE and BC solutions are equivalent
at the thermodynamic level.
