We show by means of STM that C-60 molecules can be trapped into specific sites of a 2D double-cavity open network, thus forming long-range alignments of single molecules. Since only one of the two cavities has the right size to host C-60, the smallest cavity remains empty and is thus available to trap additional species of smaller size. This novel 2D supramolecular network opens new perspectives in the design of multicomponent guest-host architectures with electronic functionalities.