Metal-organic coordination represents a versatile protocol to designed and synthesize 2D organic-based materials. When multiple binding modes are present simultaneously in the metal-organic coordination self-assembly, the outcome becomes less predictable and novel phases may emerge. Here I discuss two examples. The first system is co-existing twofold and threefold pyridyl–Cu coordination modes resulting in a demi-regular lattice which features local dodecagonal symmetry on a Cu(111) surface. This structure is thermodynamically robust and emerges solely when the molecular density is at a critical value. The second system involves Eu-carbonitrile coordination. Depending on ligand/metal stoichiometry, three-fold, four-fold, five-fold and six-fold coordination motifs can be formed on a Au(111) surface, resulting in various structures exhibiting irregular pores, square lattice, five-fold snub-square nodes structures, and hexagonal lattice. At a specific stoichiometry, the prevailing expression of five-fold and six-fold coordination nodes yields quasicrystalline tessellation. I will also discuss our recent efforts of synthesizing p-conjugated metal-organic systems exhibiting non-trivial quantum phases.