Copper based ternary and quaternary semiconductor nanostructures are of great interest for the fabrication of low cost photovoltaics. Although well-developed syntheses are available for zero dimensional (0D) nanoparticles, colloidal synthesis of two dimensional (2D) nanosheets remains a big challenge. Here we report, for the first time, a simple and reproducible cation exchange approach for 2D colloidal Cu2GeSe3, Cu2ZnGeSe4 and their alloyed Cu2GeS(x)Se(3-x), Cu2ZnGeS(x)Se(4-x) nanosheets using pre-synthesized Cu(2x)Se nanosheets as a template. A mechanism for the formation of Cu(2-x)Se nanosheets has been studied in detail. In situ oxidation of Cu(+) ions to form a CuSe secondary phase facilitates the formation of Cu(2-x)Se NSs. The obtained ternary and quaternary nanosheets have average lateral size in micrometers and thickness less than 5 nm. This method is general and can be extended to produce other important ternary semiconductor nanosheets such as CuIn(1-x)Ga(x)Se2. The optical band gap of these nanosheets is tuned from 1 to 1.48 eV, depending on their composition.