Almost stochastic dominance allows small violations of stochastic dominance rules to avoid situations where most decision makers prefer one alternative to another but stochastic dominance cannot rank them. We present the concepts of multivariate almost stochastic dominance and multivariate almost nth‐degree risk and their connections with a preference for combining good with bad. Then, we show how a preference for combining good with bad can be applied to obtain various comparative statics results, and we extend our approach to risk‐prone (convex) stochastic dominance, which relates to the opposite preference, for combining good with good and bad with bad.