Copulas are a useful tool to model multivariate distributions. While there exist various families of bivariate copulas, much fewer has been done when the dimension is higher. In this paper we propose a class of multivariate copulas based on products of transformed bivariate copulas. No constraints on the parameters refrain the applicability of the proposed class. Furthermore the analytical forms of the copulas within this class allow to naturally associate a graphical structure which helps to visualize the dependencies and to compute the likelihood efficiently even in high dimension. Numerical experiments are conducted both on simulated and real data thanks to a dedicated R package.