Covalent organic frameworks are a class of crystalline porous polymers that integrate molecular building blocks into periodic structures and are usually synthesized using two-component [1+1] condensation systems comprised of one knot and one linker. Here we report a general strategy based on multiple-component [1+2] and [1+3] condensation systems that enable the use of one knot and two or three linker units for the synthesis of hexagonal and tetragonal multiple-component covalent organic frameworks. Unlike two-component systems, multiple-component covalent organic frameworks feature asymmetric tiling of organic units into anisotropic skeletons and unusually shaped pores. This strategy not only expands the structural complexity of skeletons and pores but also greatly enhances their structural diversity. This synthetic platform is also widely applicable to multiple-component electron donor-acceptor systems, which lead to electronic properties that are not simply linear summations of those of the conventional [1+1] counterparts.