Marginal Conditional Stochastic Dominance (MCSD) developed by Shalit and Yitzhaki (1994) gives the conditions under which all risk-averse individuals prefer to increase the share of one risky asset over another in a given portfolio. In this paper, we extend this concept to provide conditions under which most (and not all) risk-averse investors behave in this way. Instead of stochastic dominance rules, almost stochastic dominance is used to assess the superiority of one asset over another in a given portfolio. Switching from MCSD to Almost MCSD (AMCSD) helps to reconcile common practices in asset allocation and the decision rules supporting stochastic dominance relations. A financial application is further provided to demonstrate that using AMCSD can indeed improve investment efficiency.