A multi-beam shape supplementary device for an antenna system for mobile communications includes a site-sharing adapter in the form of a primary adapter. The site-sharing adapter comprises at least two primary terminals for connecting at least two primary control apparatuses. The plug and/or terminal configuration or terminal occupation at the primary terminals are terminal-compatible with the terminals on the coupling terminal side of the site-sharing adapter. The pin or socket terminals provided for the bidirectional signal transmission in the site-sharing adapter are connected to a terminal pin or a terminal socket, provided for the bidirectional signal transmission, of the coupling terminal so as to form a bidirectional signal transmission path. The bidirectional transmission path is configured in such a way that the differentiated communications signals at the at least two primary terminals are converted into frequency-modulated signals.