An effective way of jointly analyzing data from multiple sources, in other words, data fusion, is to formulate the problem as a coupled matrix and tensor factorization (CMTF) problem. However, one major challenge in data fusion is that due to eclectic characteristics of data stemming from different sources, various constraints and different types of coupling between data sets should be incorporated. In this paper, we propose a flexible and efficient algorithmic framework building onto Alternating Optimization (AO) and Alternating Direction Method of Multipliers (ADMM) for coupled matrix and tensor factorizations incorporating a variety of constraints and coupling with linear transformations. Numerical experiments demonstrate that the proposed approach is accurate, computationally efficient with comparable or better performance than available CMTF methods while being also more flexible.