An electrical submersible pump assembly has a magnetic coupling between the motor shaft and the pump shaft. The coupling includes motor shaft disks mounted to the motor shaft, each having upward and downward facing disk surfaces joined by an outward facing disk cylindrical surface. Motor shaft magnets are mounted in each of the disk cylindrical surfaces and in the upward and downward facing disk surfaces. A pump shaft rotor mounted to the pump shaft has annular bands axially separated from each other by recesses into which the disks extend. Rotor magnets are mounted in each of the recess cylindrical surfaces and in upward and downward facing band surfaces. The magnets in the recesses interact with the magnets on the disks.
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