Recent advances in metabolic engineering have demonstrated that microbial biosynthesis can provide a viable alternative to chemical synthesis for the production of bulk and fine chemicals. Introduction of a new biosynthetic pathway typically requires the expression of multiple heterologous enzymes in the production host, which can impose stress on the host cell and, thereby, limit performance of the pathway. Unfortunately, analysis and treatment of the host stress response can be difficult, because there are many sources of stress that may interact in complex ways. We use a systems biological approach to analyze the stress imposed by expressing different enzyme variants from a lineage of soluble P450 monooxygenases, previously evolved for heterologous activity in Saccharomyces cerevisiae. Our analysis identifies patterns of stress imposed on the host by heterologous enzyme overexpression that are consistent across the evolutionary lineage, ultimately implicating heme depletion as the major stress. We show that the monooxygenase evolution, starting from conditions of either high or low stress, caused the cellular stress to converge to a common level. Overexpression of rate-limiting enzymes in the endogenous heme biosynthetic pathway alleviates the stress imposed by expression of the P450 monooxygenases and increases the enzymatic activity of the final evolved P450 by an additional 2.3-fold. Heme overexpression also increases the total activity of an endogenous cytosolic heme-containing catalase but not a heterologous P450 that is membrane-associated. This work demonstrates the utility of combining systems and synthetic biology to analyze and optimize heterologous enzyme expression.