So far not much configurations have been introduced with MFC, but lots have been done with MDC and each configuration has a response to either one or a couple of challenges MDC is facing.
These might help
[1] Virdis, B. et al., Microbial Fuel Cells, Treatise Water Sci., 2011 doi:10.1016/B978-0-444-53199-5.00098-1
[2] Carmalin Sophia, A., Bhalambaal, V. M., Lima, E. C. & Thirunavoukkarasu, M., Microbial desalination cell technology: Contribution to sustainable waste water treatment process, current status and future applications, J. Environ. Chem. Eng., 4 , 2016 , 3468–3478