Cooperation and competition widely exist in various kinds of network diffusions which however are usually studied separately. Recently, a novel network diffusion model, called multi-feature diffusion (MFD), attracts considerable attentions. The existing works usually assume that each feature diffuses independently and neglects the possible complex interplay between different features. In this paper, we introduce the cooperation and competition into the MFD and propose the \emph{c}ooperation and \emph{c}ompetition coupled diffusion of \emph{m}ulti-\emph{f}eature on multiplex network (CCMF). An unified framework and mathematical analytic theory regarding CCMF are then presented which are applicable and computationally efficient for any number of features and their own different sub-diffusion dynamics. In addition, an interesting finding is obtained in CCMF: compared with the high intensity competition, performing lower intensity competition under weak competition ability is more easier to result in positive effect. Due to the great importance of controlling network diffusion in many diverse contexts, we also propose an optimal allocation strategy of control resource for CCMF which first realizes the promotion and suppression of network diffusion simultaneously under one optimization framework and is also verified to be very efficient.