This paper considers the dynamics of a classical problem in astrophysics, the behavior of spherically symmetric gravitational collapse starting from a uniform, density cloud of interstellar gas. Previous work on this problem proposed a universal self-similar solution for the collapse yielding a collapsed mass much smaller than the mass contained in the initial cloud. This paper demonstrates the existence of a second threshold—not far above the marginal collapse threshold—above which the asymptotic collapse is not universal. In this regime, small changes in the initial data or weak stochastic forcing leads to qualitatively different collapse dynamics. In the absence of instabilities, a progressing wave solution yields a collapsed uniform core with infinite density. Under some conditions the instabilities ultimately lead to the well-known self-similar dynamics. However, other instabilities can cause the density profile to become non-monotone and produce a shock in the velocity. In presenting these results, we outline pitfalls of numerical schemes that can arise when computing collapse.