We address the currently open problem of existence of multiple periodic orbits in the chemostat model with periodic removal rate. We give conditions on a subset of growth functions that ensure the coexistence of an arbitrary number of species within this subset. We show that proportions of some powers of the species densities are periodic functions, leading to an infinity of distinct periodic orbits depending on the initial condition. We give also conditions allowing the coexistence of two distinct subsets of species. Although these conditions are nongeneric, we show in simulations that when these conditions are only approximately satisfied, then the behavior of the solutions are close from the non-generic case over a long time interval, justifying the interest of our study.