Flexi-MOFs are typically limited to low-connected (<9) frameworks. Here we report a platform-wide approach capable of creating a family of high-connected materials (collectively called CPM-220) that integrate exceptional framework flexibility with high rigidity. We show that the multi-module nature of the pore-space-partitioned pacs (partitioned acs net) platform allows us to introduce flexibility as well as to simultaneously impose high rigidity in a tunable module-specific fashion. The inter-modular synergy has remarkable macro-morphological and sub-nanometer structural impacts. A prominent manifestation at both length scales is the retention of X-ray-quality single crystallinity despite huge hexagonal c-axial contraction (≈ 30%) and harsh sample treatment such as degassing and sorption cycles. CPM-220 sets multiple precedents and benchmarks on the pacs platform in both structural and sorption properties. They possess exceptionally high benzene/cyclohexane selectivity, unusual C3H6 and C3H8 isotherms, and promising separation performance for small gas molecules such as C2H2/CO2.