Modular units for forming structures, such as furniture assemblies or other structures. The modular units being interconnectable by magnetic connectors that have a cage with an end cap, and a bridge connected to the cage and spaced from the end cap to define a magnet void in the cage between the end cap and the bridge. A magnet is movably positioned within void, and a magnetic mass is coupled to the cage with the bridge is between the mass and the magnet. The magnet is movable in the cage void between a shielded position held against the bridge by a first magnetic attraction between the magnet and the mass, and a locked position held against the end cap by a second magnetic attraction that is greater than the first magnetic attraction.