Bulk molecular ionic solids exhibit fascinating electronic properties, including electron correlations, phase transitions, and superconducting ground states. In contrast, few of these phenomena have been observed in low-dimensional molecular structures, including thin films, nanoparticles, and molecular blends, not in the least because most of such structures have been composed of nearly closed-shell molecules. It is therefore desirable to develop low-dimensional ionic molecular structures that can capture potential applications. Here, we present detailed analysis of monolayer-thick structures of the canonical TTF-TCNQ (tetrathiafulvalene 7,7,8,8-tetracyanoquinodimethane) system grown on low-index gold and silver surfaces. The most distinctive property of the epitaxial growth is the wide abundance of stable TTF/TCNQ ratios, in sharp contrast to the predominance of a 1:1 ratio in the bulk. We propose the existence of the surface phase diagram that controls the structures of TTF-TCNQ on the surfaces and demonstrate phase transitions that occur upon progressively increasing the density of TCNQ while keeping the surface coverage of TTF fixed. Based on direct observations, we propose the binding motif behind the stable phases and infer the dominant interactions that enable the existence of the rich spectrum of surface structures. Finally, we also show that the surface phase diagram will control the epitaxy beyond monolayer coverage. Multiplicity of stable surface structures, the corollary rich phase diagram, and the corresponding phase transitions present an interesting opportunity for low-dimensional molecular systems, particularly if some of the electronic properties of the bulk can be preserved or modified in the surface phases.