Embodiments of the invention allow performing an additive manufacturing process using a base object. Some embodiments enable placement of a three-dimensional base object inside a three-dimensional printer and print on the base object to produce a three-dimensional product. One exemplary embodiment is a method including: obtaining a representation of a three-dimensional physical object as a base object; obtaining a representation of a three-dimensional physical object as a product producible by adding layers of material on the base object. A representation of a support structure configured to retain the base object position within an additive manufacturing apparatus is determined, and the support structure is produced using an additive manufacturing process. Alternatively, a representation of an on-object structure determined and the on-object structure is produced using an additive manufacturing process by adding one or more layers of material on the base object.