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The computation of complex neutral/ionised chemical equilibrium compositions is invaluable to obtain scientific insights of, for example, the atmospheres of extrasolar planets and cool stars. We present FastChem 2, a new version of the established semi-analytical thermochemical equilibrium code FastChem. Whereas the original version is limited to atmospheres containing a significant amount of hydrogen, FastChem 2 is also applicable to chemical mixtures dominated by any other species, such as CO$_2$ or N$_2$. The new C++ code and an optional Python module are publicly available under the GPLv3 license at https://github.com/exoclime/FastChem. The program is backward compatible so that the previous version can be easily substituted. We updated the thermochemical database by adding HNC, FeH, TiH, Ca$^-$, and some organic molecules. In total 523 species are now in the thermochemical database including 28 chemical elements. The user can reduce the total number of species to, for example, increase the computation performance or can add further species if the thermochemical data are available. The program is validated against its previous version and extensively tested over an extended pressure-temperature grid with pressures ranging from $10^{-13}\,\mathrm{bar}$ up to $10^3\,\mathrm{bar}$ and temperatures between $100\,\mathrm{K}$ and $6000\,\mathrm{K}$. FastChem 2 is successfully applied to a number of different scenarios including nitrogen, carbon, and oxygen-dominated atmospheres as well as test cases without hydrogen and helium. Averaged over the extended pressure-temperature grid FastChem 2 is up to 50 times faster than the previous version and is also applicable to situations not treatable with version 1.