  It is well known that attractive condensates do not posses a stable ground
state in three dimensions. The widely used Gross-Pitaevskii theory predicts the
existence of metastable states up to some critical number
$N_{\mathrm{cr}}^{\mathrm{GP}}$ of atoms. It is demonstrated here that
fragmented metastable states exist for atom numbers well above
$N_{\mathrm{cr}}^{\mathrm{GP}}$. The fragments are strongly overlapping in
space. The results are obtained and analyzed analytically as well as
numerically. The implications are discussed.
