Interpenetration, the entwining of multiple lattices, is a common phenomenon in metal–organic frameworks (MOFs). Typically, in interpenetrated MOFs the sub-lattices are fully occupied. Here we report a family of MOFs in which one sub-lattice is fully occupied and the occupancy level of the other can be controlled during synthesis to produce frameworks with variable levels of partial interpenetration. We also report an ‘autocatenation’ process, a transformation of non-interpenetrated lattices into doubly interpenetrated frameworks via progressively higher degrees of interpenetration that involves no external reagents. Autocatenation maintains crystallinity and can be triggered either thermally or by shear forces. The ligand used to construct these MOFs is chiral, and both racemic and enantiopure partially interpenetrated frameworks can be accessed. X-ray diffraction, nonlinear optical microscopy and theoretical calculations offer insights into the structures and dynamic behaviour of these materials and the growth mechanisms of interpenetrated MOFs.