The outstanding diversity of Zr-based frameworks is inherently linked to the variable coordination geometry of Zr-oxo clusters and the conformational flexibility of the linker, both of which allow for different framework topologies based on the same linker-cluster combination. In addition, intrinsic structural disorder provides a largely unexplored handle to further expand the accessibility of novel metal-organic framework (MOF) structures that can be formed. In this work, we report the concomitant synthesis of three topologically different MOFs based on the same M6O4(OH)4 clusters (M = Zr or Hf) and methane-tetrakis(p-biphenyl-carboxylate) (MTBC) linkers. Two novel structural models are presented based on single-crystal diffraction analysis, namely, cubic c-(4,12)MTBC-M6 and trigonal tr-(4,12)MTBC-M6, which comprise 12-coordinated clusters and 4-coordinated tetrahedral linkers. Notably, the cubic phase features a new architecture based on orientational cluster disorder, which is essential for its formation and has been analyzed by a combination of average structure refinements and diffuse scattering analysis from both powder and single-crystal X-ray diffraction data. The trigonal phase also features structure disorder, although involving both linkers and secondary building units. In both phases, remarkable geometrical distortion of the MTBC linkers illustrates how linker flexibility is also essential for their formation and expands the range of achievable topologies in Zr-based MOFs and its analogues.