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 is the result of the superposition of three decoupled uniform magnetic fields. Each of them is individually generated by a different pair of Helmholtz coils. Such arrangement requires the pairs to be nested within each other, inevitably reducing the size of the working area, degrading the performance and the integration of the whole system. 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 largest working area, while keeping the different degrees of freedom balanced.