A magnetic resonance imaging (MRI) system uses a superconducting magnet having a primary coil structure and a shielding coil layer. The primary coil structure comprises at least three sets of coils with significantly different inner diameters, forming a three-bore magnet structure. The three bores are coaxially aligned with a longitudinal axis, with the largest diameter first bore on one side of the magnet and the smallest diameter third bore on another side of the magnet, as well as a medium diameter second bore located axially between the first and the third bores. The first bore allows access for the head and shoulders and permits the head to enter into the second bore for imaging, while the patient's extremities (hands, legs) may access through the third bore for producing images of the extremity joints. The magnet may also be used for other specialist imaging where use of a whole-body MRI is unwarranted, such as the imaging of neonates. Reinforcing plates can be connected between coil formers to withstand the forces generated by the high magnetic fields.