A method and apparatus for assembling multiple tire components onto one or more tire building drums at a work station of a tire building system is disclosed. A first inner set of measuring drums is located at a first loading position between a second outer set of measuring drums at a second loading position. Tire components are loaded onto the first and second sets of measuring drums at the first and second loading positions. The first and second sets of measuring drums are alternatively moved from the first and second loading positions into first and second ready positions, respectively. Then the first and second sets of measuring drums are alternatively moved from the first and second ready positions into first and second transfer positions, respectively, where the tire components are transferred to the one or more tire building drums. Then the first and second sets of measuring drums are retracted away from the first and second transfer positions, respectively, to the first and second ready positions. Finally the first and second sets of inner and outer measuring drums are alternatively moved between the first and second ready positions and the first and second loading positions so as to pass one another.