Multi-dimensional imaging techniques can provide complementary information to investigate the microscopic organizations of biological tissue. Deriving meaningful indices from these multi-dimensional imaging data is important to make these techniques relevant to clinical research. In this work, we introduce a general framework to estimate the moments of the joint probability distribution of T1, T2 relaxation and diffusion coefficients. This framework is an extension of our previously introduced REDIM approach which only focused on joint moments of T2 relaxation and diffusion. We show the cross coupling between different parameters using three datasets acquired using different protocols.