This paper presents an efficient Monte Carlo mode for simulating subcritical systems with external sources. While solving these systems as a fixed source is possible, the length of the histories grows significantly as the system nears criticality, making run time significant. Instead, a hybrid method is proposed that leverages the traditional eigensolver while including elements of the external source. The method builds on prior work,but proposes an approach that maintains the size of the source bank and also provides a natural way of scaling tallies with the true multiplication factor. The method is demonstrated on a subcritical sphere with varying point source position and energy spectrum, as well as an approach to criticality problem. The results demonstrate good agreement with the fixed-source mode, with much improved particle tracking rates for near-critical problems.