Achieving fine control on the structure of metal-organic frameworks (MOFs) is mandatory to obtain target physical properties. Herein, we present how the combination of a metalloligand approach and a postsynthetic method is a suitable and highly useful synthetic strategy to success on this extremely difficult task. First, a novel oxamato-based tetranuclear cobalt(III) compound with a tetrahedron shaped geometry is used, for the first time, as the metalloligand toward calcium(II) metal ions to lead to a diamagnetic Ca-II-Co-III three-dimensional (3D) MOF (1). In a second stage, in a single-crystal-to-single-crystal manner, the calcium(II) ions are replaced by terbium(III), dysprosium (III), holmium(III), and erbium(III) ions to yield four isostructural novel Ln(III)-Co-III [Ln = Tb (2), Dy (3), Ho (4), and Er (5)] 3D MOFs. Direct-current magnetic properties for 2-5 show typical performances for the ground-state terms of the lanthanoid cations [F-7(6)(Tb-III),I-6(15/2) (Dy-III), I-5(8) (Ho-III), and I-4(15/2) (Er-III)]. Analysis of the chi T-M data indicates that the ground state is the lowest M-J value, that is, M-J = 0 (2 and 4) and +/- 1/2 (3 and 5). Kramers' ions (3 and 5) exhibit field-induced emergent frequency-dependent alternating-current magnetic susceptibility signals, which is indicative of the presence of slow magnetic relaxation typical of single-molecule magnets.