We present the correspondence between non-interacting multi-hadron fermion star equation of state in the many-flavor limit and the degrees of freedom of a Kaluza -Klein compact star. Many flavors can be interpreted in this framework as one extra compactified spatial dimension with various, more-and-more massive hadron state excitations. The effect of increasing the degrees of freedom was investigated on the equation of state and in connection with the mass-radius relation, M (R). The maximum mass of the star, M max were also calculated as a function of the maximum number of excited states, n and the size of the compactified extra dimension, R c .