A polycarboxylate ligand, biphenyl-3,3′,4,4′-tetracarboxylic acid (H₄bptc), as an organic linker with different flexible bis(imidazole) ligands as co-ligands were selected to react with metal ions under hydrothermal conditions and six new metal–organic frameworks consisting of 1D, 2D and 3D structures were successfully isolated. Compound 1 is a fascinating self-penetrating network with the [Co₂L¹₂] loops and 2D [Co(bptc)_0.5] sheet intra-catenated (L¹ = 1,4-bis(imidazol-1-yl-methylene)-benzene). Compounds 2 and 3 feature an identical binodal 4-connected (6⁴·8²)₂(6⁵·8) net. Compound 4 is a 1D chain containing loops that further interconnected via O–H⋯O hydrogen bonds to form a 3D supramolecular framework. Compounds 5 and 6 are both corrugated 2D networks, however, the 1D [Zn(bptc)_0.5] chains are linked by [Zn₂L⁴₂] metallocycles in 5 and a pair of 1D [Cd(L⁴)]n chains in 6 (L⁴ = 1,1′-(2,2′-oxybis(ethane-2,1-diyl))bis(1-imidazole)). A comparison of all complexes demonstrates that the coordination modes of bptc⁴⁻ anions and the structural characteristics of flexible N-donor ligands simultaneously play an important role in the construction of the complexes.