Aspects of the invention provide methods and systems for moving a plurality of movable stages relative to a stator. The stator comprises a plurality of coils shaped to provide pluralities of coil trace groups where each coil trace group comprises a corresponding plurality of generally linearly elongated coil traces which extend across a stator tile. Each movable stage comprises a plurality of magnet arrays. Methods and apparatus are provided for moving the movable stages relative to the stator, where a magnet array from a first movable stage and a magnet array from a second movable stage both overlap a shared group of coil traces. For at least a portion of the time that the magnet arrays from the first and second movable stages overlap the shared group of coil traces, currents are controllably driven in the shared coil trace group based on the positions of both the first and second movable stages. The positions of the first and second movable stages may be ascertained by feedback.