Traditional carbon capture technology has been shown to effectively capture emissions, but at a cost of reducing power plant output. Molten carbonate fuel cell technology (MCFC) has the potential to be able to concentrate plant carbon emissions into a gas stream that is suitable for storage while boosting total plant power output. When considering this type of technology, the original purpose and function of the power plant must be considered. In particular, gas turbines (GT) based natural gas combined cycle (NGCC), which are capable of dynamic load following operation, are likely to need to maintain operational flexibility. This work explores the retrofit of an existing GT with MCFC technology for carbon capture when the plant is operated at part load. Physical models for major plant components are built and used to select optimal operating set points such that operating cost is minimized. Special attention is given to ensuring feasible operation across all engine components. The results show MCFC operational parameters that minimize change in fuel cell operating conditions when the gas turbine is operated at part load.