Simple Summary The cytoplasm of a living cell is a crowded place, containing hundreds of types of protein and other macromolecules. Cells reliably and continually perform thousands of biochemical reactions to maintain their health. Biomolecular condensates are fluid protein compartments that provide distinct local environments, within which they carry out cellular functions. How they prevent their contents mixing with the external environment without being encapsulated inside a lipid membrane is not fully understood. Many researchers approach this question by studying simpler systems in a test tube that contain only a few protein types although it is hard to relate their results to the complex cellular milieu. Computer simulations are used to explore the predictions of simple models of cellular behavior, but are also limited by the ability of human experimenters to recreate important aspects of the cytoplasm, in particular, its crowded nature. We have used a novel computer framework to perform dozens of simultaneous simulations that map out the influence of macromolecular crowding on the formation and structure of a biomolecular condensate. We find that the spatial structure of the model condensate is surprisingly insensitive to the composition and concentration of external macromolecules, even when its formation is assisted by steric repulsion from its environment. The crowded interior of a living cell makes performing experiments on simpler in vitro systems attractive. Although these reveal interesting phenomena, their biological relevance can be questionable. A topical example is the phase separation of intrinsically disordered proteins into biomolecular condensates, which is proposed to underlie the membrane-less compartmentalization of many cellular functions. How a cell reliably controls biochemical reactions in compartments open to the compositionally-varying cytoplasm is an important question for understanding cellular homeostasis. Computer simulations are often used to study the phase behavior of model biomolecular condensates, but the number of relevant parameters increases as the number of protein components increases. It is unfeasible to exhaustively simulate such models for all parameter combinations, although interesting phenomena are almost certainly hidden in their high-dimensional parameter space. Here, we have studied the phase behavior of a model biomolecular condensate in the presence of a polymeric crowding agent. We used a novel compute framework to execute dozens of simultaneous simulations spanning the protein/crowder concentration space. We then combined the results into a graphical representation for human interpretation, which provided an efficient way to search the model's high-dimensional parameter space. We found that steric repulsion from the crowder drives a near-critical system across the phase boundary, but the molecular arrangement within the resulting biomolecular condensate is rather insensitive to the crowder concentration and molecular weight. We propose that a cell may use the local cytoplasmic concentration to assist the formation of biomolecular condensates, while relying on the dense phase to reliably provide a stable, structured, fluid milieu for cellular biochemistry despite being open to its changing environment.