Ligand modification in MOFs provides great opportunities not only for the development of functional materials with new or enhanced properties but also for the discovery of novel structures. We report here that a sulfone-functionalized tetrahedral carboxylate-based ligand is capable of directing the formation of new and fascinating MOFs when combined with Zr4+/Hf4+ and rare-earth metal cations (RE) with improved gas-sorption properties. In particular, the resulting M-flu-SO2 (M: Zr, Hf) materials display a new type of the augmented flu-a net, which is different as compared to the flu-a framework formed by the nonfunctionalized tetrahedral ligand. In terms of properties, a remarkable increase in the CO2 uptake is observed that reaches 76.6% and 61.6% at 273 and 298 K and 1 bar, respectively. When combined with REs, the sulfone-modified linker affords novel MOFs, RE-hpt-MOF-1 (RE: Y3+, Ho3+, Er3+), which displays a fascinating (4, 12)-coordinated hpt net, based on nonanuclear [RE9(μ3-Ο)2(μ3-ΟΗ)12(-COO)12] clusters that serve as hexagonal prismatic building blocks. In the absence of the sulfone groups, we discovered that the tetrahedral linker directs the formation of new RE-MOFs, RE-ken-MOF-1 (RE: Y3+, Ho3+, Er3+, Yb3+), that display an unprecedented (4, 8)-coordinated ken net based on nonanuclear RE9-clusters, to serve as bicapped trigonal prismatic building units. Successful activation of the representative member Y-ken-MOF-1 reveals a high BET surface area and total pore volume reaching 2621 m2 g-1 and 0.95 cm3 g-1, respectively. These values are the highest among all RE MOFs based on nonanuclear clusters and some of the highest in the entire RE family of MOFs. The present work uncovers a unique structural diversity existing between Zr/Hf and RE-based MOFs that demonstrates the crucial role of linker design. In addition, the discovery of the new RE-hpt-MOF-1 and RE-ken-MOF-1 families of MOFs highlights the great opportunities existing in RE-MOFs in terms of structural diversity that could lead to novel materials with new properties.