Guest responsive porous materials represent an important and fascinating class of multifunctional solids that have attracted considerable attention in recent years. An understanding of how these structures form is essential toward their rational design, which is a prerequisite for the development of tailor-made materials for advanced applications. We herein report a novel series of stable rare-earth (RE) MOFs that show a rare continuous breathing behavior and an unprecedented gas-trapping property. We used an asymmetric 4-c tetratopic carboxylate-based organic ligand that is capable of affording highly crystalline materials upon controlled reaction with RE cations. These MOFs, denoted as RE-thc-MOF-1 (RE: Y3+, Sm3+, Eu3+, Tb3+, Dy3+, Ho3+, and Er3+), feature hexanuclear RE6 clusters that display a highly unusual connectivity and serve as unique 8-c hemi-cuboctahedral secondary building block, resulting in a new (3,3,8)-c thc topology. Extensive single-crystal to single-crystal structural analyses coupled with detailed gas (N2, Ar, Kr, CO2, CH4, and Xe) and vapor (EtOH, CH3CN, C6H6, and C6H14) sorption studies, supported by accurate theoretical calculations, shed light onto the unique swelling behavior. The results reveal a synergistic action involving steric effects, associated with coordinated solvent molecules and 2-fluorobenzoate (2-FBA) nonbridging ligands, as well as cation-framework electrostatic interactions. We were able to probe the individual role of the coordinated solvent molecules and 2-FBA ligands and found that both cooperatively control the gas-breathing and -trapping properties, while 2-FBA controls the vapor adsorption selectivity. These findings provide unique opportunities toward the design and development of tunable RE-based flexible MOFs with tailor-made properties.