Through tuning the conformations of N-donor ligands and the coordinative preferences of metal ions, three new metal–organic frameworks with different dimensionalities, namely, {[Co(L1)(bpp)(H₂O)]·0.63H₂O}_n (1), [Ni(L1)(bpp)(H₂O)(CH₃OH)]_n (2) and {Co₂(L1)₂(bpe)₂(H₂O)₂}·(H₂O)(CH₃CN)}_n (3) (H₂L1 = 1,2-bis(4-carboxy-phenoxy)ethane, bpp = 1,3–bis(4-pyridyl)propane and bpe = 1,2–bis(4-pyridyl)ethene), have been synthesized and structurally characterized. Compound 1 exhibits a 2D → 2D parallel interpenetrating motif containing two kinds of double helixes. Polymer 2 displays 2D → 3D interpenetrating framework. Compound 3 is composed of 3D unusual self-interpenetrating net with (4,6)-connected (5⁴·6⁸)(5⁶·6⁵·7²·8²) topology. This work evidently indicates that the effect of secondary ligands and geometric preferences of metal centers are critical in construction of polymeric arrangement. In addition, the stabilities of these compounds and the magnetic behaviour of 3 are discussed.