Stepped wedge design (SWD) trials are cluster randomized trials that feature staggered, unidirectional cross-over between treatment conditions. Existing literature on power for SWDs focuses primarily on designs with two conditions, typically a control and an intervention condition. However, SWDs with more than one treatment condition are being proposed and conducted. We present a linear mixed model for SWDs with two or more interventions, including both multiarm and factorial designs. We derive standard errors of the intervention effect coefficients, and present power calculation methods. We consider both repeated cross-sectional and cohort designs. Design features, with a focus on treatment allocations, are examined to determine their impact on power.