Magnetic manipulation is a method used for biomedical applications to remotely control micro-robots in a contactless manner. The electromagnet manipulator should control a magnetic field with 3 degrees of freedom inside a region of interest. In various case studies, this field results from the superposition of three decoupled uniform magnetic fields. Each of them is individually generated by a different pair of Helmholtz coils. Such an arrangement requires the pairs to be nested within each other, inevitably reducing the working area’s size and degrading the whole system’s performance and integration. The proposed work aims to design a novel electromagnetic manipulator with the help of computational design, to explore beyond the Helmholtz coils arrangement. A topology optimization framework is developed for this purpose. It investigates the distribution of coils that achieves the best field uniformity for a fixed footprint while keeping the different degrees of freedom balanced.