Cost-effective millimeter wave antennas are fundamental for the deployment of the next generation of terrestrial and satellite communication systems. The increase of the operation frequency changes the antenna design paradigm, where high gain and wide-angle beam steering are fundamental requisites. Electronic scanning approaches still face significant technological challenges, increasing the antenna costs. Therefore, low-cost designs based on mechanical steering are still relevant. The Risley prism (beam steering concept adapted from optics) is attracting significant attention in the antenna community as it can provide wide-angle azimuth and zenith beam coverage. However, this scanning mechanism tends to have high side lobe levels with typical prism implementations in the microwave domain. In this work, we use a new framework (recently proposed by the authors) based on a co-design of the phase correction of the two rotating surfaces, instead of considering each surface as a separate prism (the conventional approach). In our previous work, the improvement of SLL mitigation was demonstrated using fully dielectric TA composed of hollow square dielectric prism. However, these unit cells are far from being the optimal solution for the design transmit arrays, due to their thickness (1.4λ) and high insertion losses (1.7 dB). Herein, we design a set of multi-layer metallized unit cell with thickness 0.3 λ and insertion losses below -1 dB. We show by full-wave simulations that the previous reported SLL mitigation of the generalized Risley Prism approach is indeed a general result also effective for multi-layer TA designs.