Asymptotic giant branch (AGB) stars are major contributors to the chemical enrichment of the ISM through nucleosynthesis and extensive mass loss. Most of our current knowledge of AGB atmospheric and circumstellar chemistry, in particular in a C-rich environment, is based on observations of the carbon star IRC+10216. We aim to obtain a more generalised understanding of the chemistry in C-rich AGB CSEs by studying a sample of three carbon stars, IRAS 15194-5115, IRAS 15082-4808, and IRAS 07454-7112, and test the archetypal status often attributed to IRC+10216. We performed spatially resolved, unbiased spectral surveys in ALMA Band 3. We identify a total of 132 rotational transitions from 49 molecular species. We find that, within the uncertainties of the analysis, the observed circumstellar chemistry appears very similar across our sample and compared to that of IRC+10216, both in terms of the relative location of the emitting regions and molecular abundances. This implies that, to a first approximation, the chemical models tailored to IRC+10216 are able to reproduce the observed chemistry in C-rich envelopes across roughly an order of magnitude in wind density.