This paper describes the preparation and manipulation of several coexisting, dynamically self-assembled aggregates of millimeter-sized, magnetized disks floating at a liquid-air interface and spinning under the influence of a rotating external magnetic field. Local minima in the in-plane energy profile of these disks are created by positioning ferromagnetic needles above the plane of the interface: these needles concentrate the magnetic field locally in that plane, Spinning disks assemble in the local minima, and the positions and geometries of their aggregates can be manipulated spatially by changing the positions of the needles. Fragmentation and fusion of aggregates in response to changes in the magnetic fields are described.