A novel source convergence acceleration method for Monte Carlo eigenvalue calculations is proposed in this paper. The method consists of simulating the bulk of the inactive cycles with online-generated multigroup cross sections. Then the active cycles are simulated with continuous-energy cross sections to preserve full fidelity. The method was implemented in the Monte Carlo code SCONE and tested on several three-dimensional full-length assembly models. In some cases, the same multigroup cross sections were used for several spatially separated materials in order to limit statistical uncertainties. The method was shown to accelerate calculations by a factor of 2.5 to 5 at the cost of a slightly increased standard deviation in the flux distribution estimated across several independent simulations. The memory usage due to storing multigroup cross sections does not seem to be prohibitive for practical applications.