This is joint work with Georg Biedermann and Boris Chorny. We construct a tower of model structures on the category of functors from spaces to spaces (or spectra). The n-th stage models n-excisive homotopy functors. If the functors take values in spectra, we are able to take the fibre model structure at the n-th stage, which we show to be Quillen equivalent to the category of spectra with an action of the symmetric group on n letters.