Recent years have seen increasing attention to the subtle effects on intracellular transport caused when multiple molecular motors bind to a common cargo. We develop and examine a coarse-grained model which resolves the spatial configuration as well as the thermal fluctuations of the molecular motors and the cargo. This intermediate model can accept as inputs either common experimental quantities or the effective single-motor transport characterizations obtained through the kind of systematic analysis of detailed molecular motor models described in Fricks' presentation. Through stochastic asymptotic reductions, we derive the effective transport properties of the multiple-motor-cargo complex, and provide analytical explanations for why a cargo bound to two molecular motors moves more slowly at low applied forces but more rapidly at high applied forces than a cargo bound to a single molecular motor.