Galaxy internal structure growth has long been accused of inhibiting star formation in disc galaxies. We investigate the potential physical connection between the growth of dispersion-supported stellar structures (e.g. classical bulges) and the position of galaxies on the star-forming main sequence at z ∼ 0. Combining the might of the SAMI and MaNGA galaxy surveys, we measure the λRe spin parameter for 3289 galaxies over 9.5<logM⋆[M⊙]<12. At all stellar masses, galaxies at the locus of the main sequence possess λRe values indicative of intrinsically flattened discs. However, above logM⋆[M⊙]∼10.5 where the main sequence starts bending, we find tantalizing evidence for an increase in the number of galaxies with dispersion-supported structures, perhaps suggesting a connection between bulges and the bending of the main sequence. Moving above the main sequence, we see no evidence of any change in the typical spin parameter in galaxies once gravitationally interacting systems are excluded from the sample. Similarly, up to 1 dex below the main sequence, λRe remains roughly constant and only at very high stellar masses (logM⋆[M⊙]>11), do we see a rapid decrease in λRe once galaxies decline in star formation activity. If this trend is confirmed, it would be indicative of different quenching mechanisms acting on high- and low-mass galaxies. The results suggest that whilst a population of galaxies possessing some dispersion-supported structure is already present on the star-forming main sequence, further growth would be required after the galaxy has quenched to match the kinematic properties observed in passive galaxies at z ∼ 0.