Whether or not there is room in the Pentagon, think this as getting bureaucrapts out of DC and into the hinterland and make them live with “common folk.”
Regarding “room in the Pentagon” the military command structure and bureaurcracy exceeded the capacity of the Pentagon many decades ago, probably around 1960. When I first went there in 1981, there were entire DoD organizations in a dedicated set of at least 6 high rise buildings know as Crystal City. It was just across I-395 on the south side of the Pentagon. I was in the actual Pentagon building, in the 2nd sub-basement for 2 years in the Army Operations Center. It was a pretty good assignment. I arrived as a SSG and departed as a CPT.
The heads of the other service branches is in D.C. Move Space Command to the sticks makes it an adjunct of another branch, probably the Air Force.