Molecular motors are proteins in biological cells which perform various sorts of biophysical work. The microscale physics of their operation motivates inherently stochastic models, both for their binding kinetics as well as for their spatial motion. The molecular motor kinesin, on which we will focus, carries a load on its tail while its head walks along microtubule filaments. We revisit two paradigms of cooperative action by kinesin molecular motors. First, we extend consideration of gliding assays to a situation where microtubules are crosslinked while being crowdsurfed by immobilized kinesin. Second, for two dissimilar types of kinesin transporting a common cargo, we provide approximate analytical characterizations for how incorporating slack in the tether model affects the cooperative dynamics.