alternate

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alternate between (someone and someone else)

 and alternate between something and something else
to 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.
See also: alternate

alternate with something

 
1. [for someone] to serve as a substitute for someone. I alternated with Fred as the lead in the school play. They asked Harry to alternate with Ron on the team.
2. [for something] to appear repetitively and regularly in a sequence with something else. (For instance, A alternates with B in the sequence ABABAB.) In this design the straight lines alternate with the circles. The red dots alternate with the blue ones.
See also: alternate