We use a 2D finite‐element program to investigate how effects of time‐dependent pore pressure and off‐fault damage in the form of plastic yielding could affect earthquake rupture on parallel strike‐slip faults with a stepover. From single‐fault tests, we find that the positive Coulomb stress (PCS) region at the end of the first fault controls the rupture initiation time and location on the second fault. Plastic deformation could significantly reduce the effective normal stress and adjust the shear stress in a specific direction, resulting in a narrowband with PCS in a dilatational stepover favoring the initiation of rupture. For a compressive stepover, the effect of plastic deformation is less obvious and the crescent‐shaped PCS region triggers rupture initiation on the second fault. The undrained pore pressure increases the effective normal stress in a dilatational stepover, which significantly reduces the jumping ability of rupture. When both undrained pore pressure and significant off‐fault damage are present, the effect of undrained pore pressure dominates in the dilatational stepover, whereas plastic deformation in the compressive stepover slightly reduces the maximum jumpable width.