Compared with modularized enterprises, continuous Process (CP) enterprises exhibit differing characteristics in manufacturing flexibility. Relative to the vast literature on the flexibility of modularized enterprises, the manufacturing flexibility of CP enterprises has aroused little attention in current literature. In this paper, we develop a new theory to give a reasonable explanation for the flexible manufacturing problem of CP enterprises with multiple products. Based on the analysis of flexible manufacturing process of Jiahua enterprise, we find that CP enterprises can create product diversity through component flexibility, control flexibility and mixed flexibility. The discussion on the permutoid, arising from the product production transformation process of CP enterprises, further reveals the possibility of cost reduction in production transformation and thus efficiency enhancement of manufacturing flexibility. The cost-efficient flexibility of CP enterprises is realized by properly scheduling the production process, shortening the continuous transforming time of the permutoid and reverse development of the permutoid, with exploiting the characteristics of compatibility, continuity and reversibility of the permutoid. Finally, we conclude that the study on the manufacturing flexibility of CP enterprises will contribute to the flexible production transformation in the industries with CP.