Transport of intracellular cargos by multiple microtubule motor proteins is believed to be a common and significant phenomenon in vivo, yet signatures of the microscopic dynamics of multiple motor systems are only now beginning to be resolved. Understanding these mechanisms largely depends on determining how grouping motors affect their association with microtubules and stepping rates, and hence, cargo run lengths and velocities. We examined this problem using a discrete state transition rate model of collective transport. This model accounts for the structural and mechanical properties in binding/unbinding and stepping transitions between distinct microtubule-bound configurations of a multiple motor system. In agreement with previous experiments that examine the dynamics of two coupled kinesin-1 motors, the energetic costs associated with deformations of mechanical linkages within a multiple motor assembly are found to reduce the system's overall microtubule affinity, producing attenuated mean cargo run lengths compared to cases where motors are assumed to function independently. With our present treatment, this attenuation largely stems from reductions in the microtubule binding rate and occurs even when mechanical coupling between motors is weak. Thus, our model suggests that, at least for a variety of kinesin-dependent transport processes, the net 'gains' obtained by grouping motors together may be smaller than previously expected.