Intersecting orthogonal strike‐slip faults with opposite senses of slip pose the question of what allows rupture to propagate through the junction and through both faults versus confining rupture to a single fault. I conduct dynamic rupture simulations on simplified orthogonal strike‐slip fault systems, to determine which conditions produce rupture on both component faults. In models with uniform initial tractions on both faults, slip on the first fault must reduce normal stress on the second fault for it to rupture. If the first fault ends at the cross fault, a stopping phase causes the cross fault to rupture. In models where I resolve a uniform regional stress field on the faults, only a narrow range of stress orientations allow multifault ruptures. These results will be helpful for evaluating hazard near orthogonal strike‐slip faults. Plain Language Summary There are many examples around the world where two strike‐slip earthquake faults cross each other at nearly 90° angles. This is not remarkable when only one of the faults in a pair causes an earthquake, but it becomes notable when two or more crossing faults move at the same time. This raises the question of what causes the second fault to get involved, or not. To address this question, I use computer simulations of the physics of the earthquake process to test dozens of different fault configurations and earthquake starting points. I find that the location where the earthquake starts on the first fault controls whether the second fault is made stronger versus weaker, and therefore whether both faults can move together in one earthquake. These results can help us understand earthquake hazard around crossing faults. Key Points Nucleation location effectively controls whether multifault rupture occurs on orthogonal strike‐slip fault systems A stopping phase from rupture reaching the end of one fault is often required to initiate rupture on the cross fault Only a narrow range of regional stress orientations allows both cross‐faults to rupture