Multicomponent metal-organic frameworks (MOFs) promise the precise placement of synergistic functional groups with atomic-level precision, capable of promoting fascinating developments in basic sciences and applications. However, the complexity of multicomponent systems poses a challenge to their structural design and synthesis. Herein, we show that linkers of low symmetry can bring new opportunities to the construction of multicomponent MOFs. A carbazole-tetracarboxylate linker of C-s point group symmetry was designed and combined with an 8-connected Zr-6 cluster to generate a low-symmetry MOF, PCN-609. PCN-609 contains coordinatively unsaturated Zr sites arranged within a lattice with three crystallographically distinct pockets, which can accommodate linear linkers of different lengths. Sequential linker installation was carried out to postsynthetically insert three linear linkers into PCN-609, giving rise to a quinary MOF. Functionalization of each linker from the quinary MOF system creates multivariate pore environments with unprecedented complexity.