The search for porous materials with strong Brønsted acid sites for challenging reactions has long been of significant interest, but it remains a formidable synthetic challenge. Here we demonstrate a cage extension strategy to construct chiral permanent porous hydrogen-bonded frameworks with strong Brønsted acid groups for heterogeneous asymmetric catalysis. We report the synthesis of two octahedral coordination cages using enantiopure 4,4',6,6'-tetra(benzoate) ligand of 1,1'-spirobiindane-7,7'-phosphoric acid and Ni4/Co4-p-tert-butylsulfonylcalix[4]arene clusters. Intercage hydrogen-bonds and hydrophobic interactions between tert-butyl groups direct the hierarchical assembly of the cages into a permanent porous material. The chiral phosphoric acid-containing frameworks can be high efficient and recyclable heterogeneous Brønsted acid catalysts for asymmetric [3+2] coupling of indoles with quinone monoimine and Friedel-Crafts alkylations of indole with aryl aldimines. The afforded enantioselectivities (up to 99.9% ee) surpass those of the homogeneous counterparts and compare favorably with those of the most enantioselective homogeneous phosphoric acid catalysts reported to date.