Conventional processes are being pushed to their limits by growing demands in terms of sustainability and diversity of variants. Hybrid components, which are produced by a combination of two or more manufacturing processes, are a suitable way of meeting these challenges. The combination of sheet metal forming processes with additive manufacturing offers the potential to link personalized components with standardized parts. Knowing that the additively manufactured components influence the forming process, it is essential to understand the interactions in detail. Therefore, this work will compare the influence of several additively manufactured elements (AME) for deep drawing with two different punch geometries. The approach used combines experimental and numerical investigations to improve process insight in relation to sheet metal forming of hybrid components. The results show that the AMEs amplify existing stresses and strains in dependence of the present load. Sections subjected to low loads, as it is found in the bottom of the cup manufactured with a cylindrical punch, are hardly affected, whereas stronger loaded areas, e.g. the center of the parts manufactured with a hemispherical punch, are affected all the more.