The star-formation rate in galaxies is well known to correlate with stellar mass (the ‘star-forming main sequence’). Here, we extend this further to explore any additional dependence on galaxy surface brightness, a proxy for stellar mass surface density. We use a large sample of low-redshift (z ≤ 0.08) galaxies from the Galaxy And Mass Assembly survey which have both spectral energy distribution (SED) derived star-formation rates and photometric bulge-disc decompositions, the latter providing measures of disc surface brightness and disc masses. Using two samples, one of galaxies fitted by a single component with Sérsic index below 2 and one of the discs from two-component fits, we find that once the overall mass dependence of star-formation rate is accounted for, there is no evidence in either sample for a further dependence on stellar surface density.