We identify a taxonomic property on the growth functions in the multi-species chemostat model which ensures the coexistence of a subset of species under periodic removal rate. We show that proportions of some powers of the species densities are periodic functions, leading to an infinity of distinct neutrally stable periodic orbits depending on the initial condition. This condition on the species for neutral stability possesses the feature to be independent of the shape of the periodic signal for a given mean value. We give also conditions allowing the coexistence of two distinct subsets of species. Although these conditions are non-generic, we show in simulations that when these conditions are only approximately satisfied, then the behavior of the solutions is close from the non-generic case over a long time interval, justifying the interest of our study.