alternate between
To switch between two different people or things. We are going to alternate between the lead and the understudy at today's rehearsal. The air conditioner alternates between settings, so I don't think it will get too cold in here.
alternate between (someone and someone else)
and alternate between something and something elseto choose or change between two persons or things alternately. The job will alternate between Gil and Ed. The maid will alternate between the first floor and the second floor.