ABSTRACT Sun-like stars are a new probe of variations in the fine-structure constant, α, via the solar twins approach: velocity separations of close pairs of absorption lines are compared between stars with very similar stellar parameters, i.e. effective temperature, metallicity, and surface gravity within 100 K, 0.1 dex, and 0.2 dex of the Sun’s values. Here, we assess possible systematic errors in this approach by analysing ≳10 000 archival exposures from the High-Accuracy Radial Velocity Planetary Searcher (HARPS) of 130 stars covering a much broader range of stellar parameters. We find that each transition pair’s separation shows broad, low-order variations with stellar parameters that can be accurately modelled, leaving only a small residual, intrinsic star-to-star scatter of 0–33 m s−1 (average ≈7 m s−1, ≈1 × 10−4 Å at 5000 Å). This limits the precision available from a single pair in a single star. We consider potential systematic errors from a range of instrumental and astrophysical sources (e.g. wavelength calibration, charge transfer inefficiency, stellar magnetic activity, line blending) and conclude that variations in elemental abundances, isotope ratios, and stellar rotational velocities may explain this star-to-star scatter. Finally, we find that the solar twins approach can be extended to solar analogues – within 300 K, 0.3 dex, and 0.4 dex of the Sun’s parameters – without significant additional systematic errors, allowing a much larger number of stars to be used as probes of variation in α, including at much larger distances.