Heterogeneity is an inherent feature of the glycosylation process. Mammalian cells often produce a variety of glycan structures on separate molecules of the same protein, known as glycoforms. This heterogeneity is not random but is controlled by the organization of the glycosylation machinery in the Golgi cisternae. In this work, we use a computational model of the N-glycosylation process to probe how the organization of the glycosylation machinery into different cisternae drives N-glycan biosynthesis toward differing degrees of heterogeneity. Using this model, we demonstrate the N-glycosylation potential and limits of the mammalian Golgi apparatus, for example how the number of cisternae limits the goal of achieving near homogeneity for N-glycans. The production of specific glycoforms guided by this computational study could pave the way for "glycoform engineering," which will find uses in the functional investigation of glycans, the modulation of glycan-mediated physiological functions, and in biotechnology.