High-quality magnetic resonance imaging and spectroscopic measurements require a highly homogeneous magnetic field. However, both static and dynamic variations in the main magnetic field (B0) cause various artifacts. These artifacts can be corrected by providing a compensating magnetic field generated by shim coils. Different from correcting global magnetic field inhomogeneity by large volume shim coils, localized off-resonance can be corrected by using multiple shim coils. Previously, arrays of circular shim coils and integrated radio-frequency (RF)-shimming coils have been implemented. However, these designs cause non-negligible interference to RF coils and consequent image quality degradation. Here we propose a new design of multi-coil shimming, where shim coils and nearby RF coils are arranged on two orthogonal planes. This orthogonal positioning minimizes the interference between RF coils and shim coils, while multiple shim coils provide similar shimming performance like previous multi-coil shim array designs. We use both simulatiosn and phantom experiments to demonstrate the feasibility of this design.