Current research on control allocation emphasizes reconfiguration for adapting to thruster failures. However, in the application of autonomous assembly, the reconfiguration is necessitated by changing physical properties. For the scenario of an assembler tug constructing a large space structure, every docking and undocking maneuver used for the tug to move an individual payload causes a large shift in the dynamics of the tug. Not only do the mass properties change, but so does the thruster configuration. Changes in the center of mass, mass, and inertia of the tug-payload system, causes changes in the equivalent force exerted by each thruster. This paper explores reconfigurable control allocation to adapt to changes in the mass properties. Specifically considered are changes to the center of mass and thruster configuration (number, location, and active thrusters). Results are presented from the implementation of a reconfigurable control allocation algorithm on the SPHERES (Synchronized Position Hold Engage Reorient Experimental Satellites) testbed aboard the International Space Station. Results demonstrate controllability for configurations with large center of mass shifts, varying number of thrusters, as well as maintaining performance from the baseline non-reconfigurable control allocation algorithm on SPHERES.