We demonstrate sequential assembly of chemically patchy colloids such that their valence differs from stage to stage to produce hierarchical structures. For proof of concept, we employ ACB triblock spheres suspended in water, with the C middle band electrostatically repulsive. In the first assembly stage, only A-A hydrophobic attraction contributes, and discrete clusters form. They can be stored, but subsequently activated to allow B-B attractions, leading to higher-order assembly of clusters with one another. The growth dynamics, observed at a single particle level by fluorescence optical microscopy, obey the kinetics of stepwise polymerization, forming chains, pores, and networks. Between linked clusters, we identify three possible bond geometries, linear, triangular, and square, by an argument that is generalizable to other patchy colloid systems. This staged assembly strategy offers a promising route to fabricate colloidal assemblies bearing multiple levels of structural and functional complexity.