  For a 1-connected spectrum E, we study the moduli space of suspension spectra
which come equipped with a weak equivalence to E. We construct a spectral
sequence converging to the homotopy of the moduli space in positive degrees. In
the metastable range, we get a complete homotopical classification of the path
components of the moduli space. Our main tool is Goodwillie's calculus of
homotopy functors.
