Intracellular transport is a fundamental biological process during which cellular materials are driven by enzymatic molecules called motor proteins. Recent optical trapping experiments and theoretical analysis have uncovered many features of cargo transport by multiple kinesin motor protein molecules under applied loads. These studies suggest that kinesins cooperate negatively under typical transport conditions, although some productive cooperation could be achieved under higher applied loads. However, the microscopic origins of this complex behavior are still not well understood. Using a discrete-state stochastic approach we analyze factors that affect the cooperativity among kinesin motors during cargo transport. Kinesin cooperation is shown to be largely unaffected by the structural and mechanical parameters of a multiple motor complex connected to a cargo, but much more sensitive to biochemical parameters affecting motor-filament affinities. While such behavior suggests the net negative cooperative responses of kinesins will persist across a relatively wide range of cargo types, it is also shown that the rates with which cargo velocities relax in time upon force perturbations are influenced by structural factors that affect the free energies of and load distributions within a multiple kinesin complex. The implications of these later results on transport phenomena where loads change temporally, as in the case of bidirectional transport, are discussed.