Composite Higgs: searches for new physics at future $e^+e^-$ colliders

In this proceeding, we extend a previous analysis concerning the prospects of a future electron-positron collider in testing the 4-Dimensional Composite Higgs Model. In particular, we introduce two motivated benchmarks and study them in Higgs-Strahlung, for three possible energy stages and different luminosity options of such a machine and confront our results to the expected experimental accuracies in the various accessible Higgs decay channels.