[en] Recently, attention has focused on the effects of spherical convergence on the nonlinear phase of Rayleigh-Taylor growth. In particular, for instability growth on spherically converging interfaces, modifications to the predictions of the Layzer model for the secular growth of a single, nonlinear mode have been reported. On the other hand, applications of interest involve surface perturbations which include the superposition of many unstable modes growing simultaneously. Such weakly nonlinear, multimode growth has previously been studied in the context of the well-known Haan model. Here, we combine the most recent results for enhanced nonlinear single mode growth on spherical interfaces with the Haan model formulation for multimode growth. Remarkably, the multimode results are found not to be substantially modified by including the effects of convergence