We propose a new model for determining the set of plausible multifault ruptures in an interconnected fault system. We improve upon the rules used in the Third Uniform California Earthquake Rupture Forecast (UCERF3) to increase connectivity and the physical consistency of ruptures. We replace UCERF3’s simple azimuth change rules with new Coulomb favorability metrics and increase the maximum jump distance to 15 km. Although the UCERF3 rules were appropriate for faults with similar rakes, the Coulomb calculations used here inherently encode preferred orientations between faults with different rakes. Our new rules are designed to be insensitive to discretization details and are generally more permissive than their UCERF3 counterparts; they allow more than twice the connectivity compared to UCERF3, yet heavily penalize long ruptures that take multiple improbable jumps. The set of all possible multifault ruptures in the California fault system is near-infinite, but our model produces a tractable set of 326,707 ruptures (a modest 29% increase over UCERF3, despite the greatly increased connectivity). Inclusion in the rupture set does not dictate that a rupture receives a significant rate in the final model; rupture rates are subsequently determined by data constraints used in an inversion. We describe the rupture building algorithm and its components in detail and provide comparisons with ruptures generated by a physics-based multicycle earthquake simulator. We find that greater than twice as many ruptures generated by the simulator violate the UCERF3 rules than violate our proposed model.