G-quadruplexes can multimerize under certain conditions, but the sequence requirements of such structures are not well understood. In this study, we investigated the ability of all possible variants of the central tetrad in a monomeric, parallel-strand G-quadruplex to form higher-order structures. Although most of these 256 variants existed primarily as monomers under the conditions of our screen, ∼10% formed dimers or tetramers. These structures could form in a wide range of monovalent and divalent metal ions, and folding was highly cooperative in both KCl and MgCl2. As was previously shown for G-quadruplexes that bind GTP and promote peroxidase reactions, G-quadruplexes that form dimers and tetramers have distinct sequence requirements. Some mutants could also form heteromultimers, and a second screen was performed to characterize the sequence requirements of these structures. Taken together, these experiments provide new insights into the sequence requirements and structures of both homomultimeric and heteromultimeric G-quadruplexes.