Can we use imitation learning for on-policy algorithms?

Imitation learning uses experiences of an (expert) agent to train another agent, in my understanding. If I want to use an on-policy algorithm, for example, Proximal Policy Optimization, because of it’s on-policy nature we cannot use the experiences generated by another policy directly. Importance Sampling can be used to overcome this limitation, however, it is known to be highly unstable. How can imitation learning be used for such on-policy algorithms avoiding the stability issues?