Someone suggested in the comments that the other side of the door with the two foot drop might have another two foot drop, thus actually making some sort of sense. That’s pretty close! It turns out to be home to a nuclear magnetic resonance imaging system used by all the members of the Gulf Coast Consortium, a teaching and research collaborative formed in 2001 by Rice, the Baylor College of Medicine, the University of Houston, the University of Texas Health Science Center-Houston, the University of Texas Medical Branch at Galveston and the University of Texas M. D. Anderson Cancer Center.
It’s a huge, heavy machine and back in 2004 they had to use a big crane to lower it into the space through the roof. Here’s a picture stolen from the Biochemistry and Cell Biology web site–if you look closely at the top of the photo, you can see the bottom of the door up in the middle of the wall.