The paper is organized as follows. The relevant theoretical background is given in Sec-tion 2. The behavior of MRF for uniformly scaled densities and the uniform electron gas are then studied in Sections 3 and 4, respectively. These insights are then used in Section 5 to analyze how MRF can be improved. The details for the implementation of MRF are given in Section 6, discussion and numerical examples are given in Section 7, while Section 8 is devoted to conclusions and outlooks.