We report the synthesis of two catenane-containing struts that are composed of a tetracationic cyclophane (TC4+) encircling a 1,5-dioxynaphthalene (DNP)-based crown ether, which bears two terphenylene arms. The TC4+ rings comprise either 1) two bipyridinium (BIPY2+) units or 2) a BIPY2+ and a diazapyrenium (DAP2+) unit. These degenerate and nondegenerate catenanes were reacted in the presence of Cu(NO3)2⋅2.5 H2O to yield Cu-paddlewheel-based MOF-1050 and MOF-1051. The solid-state structures of these MOFs reveal that the metal clusters serve to join the heptaphenylene struts into grid-like 2D networks. These 2D sheets are then held together by infinite donor–acceptor stacks involving the catenanes to produce interpenetrated 3D architectures. As a consequence of the planar chirality associated with both the DNP and hydroquinone (HQ) units present in the crown ether, each catenane can exist as four stereoisomers. In the case of the nondegenerate (bistable) catenane, the situation is further complicated by the presence of translational isomers. Upon crystallization, however, only two of the four possible stereoisomers—namely, the enantiomeric RR and SS forms—are observed in the crystals. An additional element of co-conformational selectivity is present in MOF-1051 as a consequence of the substitution of one of the BIPY2+ units by a DAP2+ unit: only the translational isomer in which the DAP2+ unit is encircled by the crown ether is observed. The overall topologies of MOF-1050 and MOF-1051, and the selective formation of stereoisomers and translational isomers during the kinetically driven crystallization, provide evidence that weak noncovalent bonding interactions play a significant role in the assembly of these extended (super)structures.