2D lamellar membranes (2DLMs) are used for efficient desalination and nanofiltration. However, weak interactions between adjacent stacked nanosheets result in susceptibility to swelling that limits practical applicability. Inspired by the super adhesion of multi-point suction cups on octopus tentacles, a 2DLM is constructed from Ti₃ C₂ T_x MXene supported by the macrocyclic "multi-point" molecule cucurbit[5]uril (CB5) and demonstrated for nanofiltration of methyl blue (MB) and enrichment of uranyl carbonate. Experimental results and density functional theory calculations indicate that CB5 rivets to the surface of the nanoflakes through strong stable interactions between its multiple binding sites and surface hydroxyl functional groups on MXene nanosheets. This novel 2DLM exhibits excellent nanofiltration performance (69 L m^-2 h^-1 bar^-1 permeance with 93.6% rejection for MB) and can be recycled at least 30 times without significant degradation. The 2DLM exhibits excellent swelling resistance at high salinity, with a demonstration of selective enrichment of uranyl carbonate from artificial water and natural seawater. The results provide a new strategy for constructing highly stable 2DLMs with interlayer spacing controllable from sub-nano to nanometer scales, for size-selective sieving of molecules and ions, high-efficiency nanofiltration, and other applications.