The single-material overlapping models are incompatible with multi-material wire arc additive manufacturing (WAAM). A newly developed generalised model considers dissimilar adjoining beads in multi-material WAAM. The geometric model of dissimilar overlapping beads coupled with an algorithm identifies the process conditions for the two materials to maintain the same bead heights. The model, implemented for stainless-steel and creep-resistant-steel pair, yields significant scientific and practical findings. Compared to a fixed overlapping distance in single-material, e.g. 0.66 or 0.738 times the bead width, the multi-material overlapping distance is a complex function of individual bead widths. The bi-metallic interface fusion is affected by the molten metal flow, bead dimensions, and heat input. Contrary to the prevailing notion of a flat-top surface in the intermediate layer ideal for multi-layer deposition, a slight hill ensures a defect-free interface. The repeatable and defect-free bi-metallic walls and matrix is expected to have a breakthrough in multi-material WAAM.