They both have some relationship with the main characters.
Like the units MARs, Happy Rain♪, SoLaMi♡SMILE, TRiANGLE and MY☆DREAM, WITH is a unit consisting of a lovely type idol, a pop type idol and a cool type idol. Like the above mentioned units, WITH has a lovely type idol as the center.
According to a special interview, Koyoi is the leader of WITH. He started it with Asahi at first, and then Shougo got recruited later on.