On the James Webb Space Telescope (JWST), the Mid-Infrared Instrument (MIRI) is unique among the four science instruments in that it operates around 7K as opposed to 40K like the other three near infrared instruments. Remote cooling of the MIRI is achieved through the use of a Joule-Thomson (J-T) Cooler, which is precooled by a multistage Pulse Tube Cooler. The MIRI Cooler systems engineering is elaborate because the Cooler spans a multitude of regions in the observatory that are thermally and mechanically unique with interfaces that encompass a number of different organizations. This paper will discuss how a significant change to the MIRI Cooling System from a solid hydrogen Dewar to a Cooler was achieved after the instrument Preliminary Design Review (PDR), and it will examine any system compromises or impacts that resulted from this change so late in the instrument design. A general overview of the Dewar and the Cooler systems management, the roles of the systems teams in the different organizations, how the requirements are managed in such an elaborate environment, and the distinct design and Integration and Test (I&T) challenges will also be provided.