Differential Evolution (DE) is recognized as one of the most powerful optimizers in the evolutionary algorithm (EA) family. Many DE variants were proposed in recent years, but significant differences in performances between them are hardly observed. Therefore, this paper suggests a multi-layer competitive-cooperative (MLCC) framework to facilitate the competition and cooperation of multiple DEs, which in turns, achieve a significant performance improvement. Unlike other multi-method strategies which adopt a multi-population based structure, with individuals only evolving in their corresponding subpopulations, MLCC implements a parallel structure with the entire population simultaneously monitored by multiple DEs assigned to their corresponding layers. An individual can store, utilize and update its evolution information in different layers based on an individual preference based layer selecting (IPLS) mechanism and a computational resource allocation bias (RAB) mechanism. In IPLS, individuals connect to only one favorite layer. While in RAB, high-quality solutions are evolved by considering all the layers. Thus DEs associated in the layers work in a competitive and cooperative manner. The proposed MLCC framework has been implemented on several highly competitive DEs. Experimental studies show that the MLCC variants significantly outperform the baseline DEs as well as several state-of-the-art and up-to-date DEs on CEC benchmark functions.