The original organizational evolutionary algorithm (OEA) is often trapped in local optima when optimizing multimodal functions with high dimensions. In this paper, following an analysis of the main causes of the premature convergence, it proposes a novel algorithm, called the multipoint organizational evolutionary algorithm (mOEA). To discourage the premature convergence, a crossover strategy of multiple points is designed to achieve a better diversity of leader population. Inspired by the cognition and learning physics of social swarms, an improved annexing operator enables members in an organization to either partially climb around their leader or randomly mutate within the search range. The new annexing manipulation both enhances fitness values and preserves a good diversity of member population. Experiments on six complex optimization benchmark functions with 30 or 100 dimensions and very large numbers of local minima show that, comparing with the original OEA and CLPSO, mOEA effectively converges faster, results in better optima, is more robust.