As per my knowledge, eNodeB performs load balancing between the MMEs connected to the eNodeB.
In S1 SETUP RESPONSE message, each MME reponds with its "Relative MME capacity" to the eNodeB.
If MME still gets overloaded, it sends OVERLOAD START message with the action need to be taken at eNodeB for the further incoming signalling (RRC Connection Request) from the UEs.
With respect to your question, MME can initiate "UE Context Release procedure " for some of the selected UEs to move them to another MME. To achieve this, MME sends "UE CONTEXT RELEASE COMMAND" message to enodeB with the cause "Load balancingTAU" required.
Once the MME receives this UE Context Release Command message from the MME, it initiates RRC Connection Release procedure for that UE by sending RRC Connection Release message to UE with the cause "LoadbalacningTAU".