Differential evolution (DE) is recognized as a simple but powerful algorithm in the family of evolutionary algorithms. Over the past two decades, many advanced DE variants with significantly improved performance have been proposed. However, the variants may only achieve the best performance on a certain type of functions. Moreover, a specific optimizer may not always be suitable for the whole optimization process. To overcome these weaknesses, this paper proposes a multiple variants coordination (MVC) framework with two mechanisms, namely, the multiple variants adaptive selecting mechanism and the multiple variants adaptive solutions preserving mechanisms (MV-APM). In MVC, the evolution process is divided into nonoverlap segments with equal numbers of generations. Each segment includes the learning generations (LGs) and executing generations (EGs). In LG, all the candidate DE optimizers are utilized independently. The best performing optimizer is determined and then utilized in EG in the same segment. Furthermore, MV-APM maintains the population by adaptively preserving promising solutions generated by multiple optimizers. Numerical experiments on the CEC2014 benchmark suit show that the proposed MVC framework can significantly improve the performance of the baseline algorithms and the resulted algorithm significantly outperform the start-of-the-art and up-to-date DEs. Moreover, as a general framework, MVC can also be applied to coordinate multiple improved DE variants to further enhance their performance.