Reactions in water between mixtures of rare earth ions (Ln = Y, La-Tm, except Pm) and the sodium salt of terephthalic acid lead to an infinite family of isostructural heteropolynuclear coordination polymers. The monophasic character of the synthesized powders as well as the isostructurality of the heteropolynuclear compounds with the previously described mononuclear [Tb-2(C8H4O4)(3)(H2O)(4)](infinity) are ascertained on the basis of the X-ray powder diffraction diagrams. One family of heterodinuclear compounds has been studied in detail, that is, [(La2-xYx)(C8H4O4)(3)(H2O)(4)](infinity) with 0 <= x <= 2. This study demonstrates the random character of the spatial distribution of the metallic ions. In order to demonstrate the high modularity of the physical properties, the solid-state luminescent properties of the compounds of general formula [(Eu2-xTbx)(C8H4O4)(3)(H2O)(4)](infinity) with 0 <= x <= 2 have been studied and compared to those of the corresponding mixtures of [(Eu-2)(C8H4O4)(3)(H2O)(4)](infinity) and [(Tb-2)(C8H4O4)(3)(H2O)(4)](infinity). In order to confirm the general character of these studies, the compound containing in equal proportions all 13 rare earth ions between La and Tm (except Pm) plus Y has been synthesized and characterized. At last, the solid-state luminescent properties of compounds belonging to the ternary system [(Ce2-x-yEuxTby)(C8H4O4)(3)(H2O)(4)](infinity) with x + y <= 2 are briefly described.