The Td point group symmetry of rare earth (RE3+) metal clusters RE4(mu3-OH)4(COO)62+ makes them attractive building blocks for creating metal-organic frameworks (MOFs) with controllable topologies. Herein, we describe the design and synthesis of a series of isoreticular MOFs featuring pcu topology [MOF-1114(RE) and MOF-1115(RE)] with variable rare earth metal ions (RE3+ = Y3+, Sm3+, Eu3+, Gd3+, Tb3+, Dy3+, Ho3+, Er3+, Tm3+, Yb3+) and linear amino-functionalized dicarboxylate linkers of different lengths. In total, we report 22 MOFs that vary in both composition and structure yet share the same RE4(mu3-OH)4 cluster motif. We demonstrate that these pcu MOFs are cationic and that anion exchange can be used to affect the MOF properties. We also investigate the luminescence properties of a representative member of this MOF series [MOF-1114(Yb)] that exhibits near-infrared emission. We show that the excitation energy for Yb3+ sensitization can be carefully adjusted to lower energy via covalent postsynthetic modification at the amino group sites within the MOF.