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This paper reports the results of the second phase of a research project to characterize and optimize the design of an advanced launch vehicle for human access to low earth orbit. The vehicle makes use of rocket-based combined-cycle (RBCC) propulsion - a concept combining operating modes of an ejector, ramjet, scramjet, and rocket in a single engine. This research builds on previous work focused on advanced multiple mode propulsion concepts and advanced conical acceleration-class single-stage-to-orbit (SSTO) launch vehicles. Three systems level design variables of interest were optimized using multidisciplinary design optimization (MDO) techniques. Specifically, Taguchi's method of robust design was used to identify a combination of variables that minimize the vehicle sensitivity to unpredictable changes in engine weights and performance. In addition, a second-order response surface method (RSM) was used to approximate the design space and predict the minimum dry weight vehicle.