  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
$z\sim0$. Combining the might of the SAMI and MaNGA galaxy surveys, we measure
the $\lambda_{Re}$ spin parameter for 3781 galaxies over $9.5 < \log M_{\star}
[\rm{M}_{\odot}] < 12$. At all stellar masses, galaxies at the locus of the
main sequence possess $\lambda_{Re}$ values indicative of intrinsically
flattened discs. However, above $\log M_{\star}[\rm{M}_{\odot}]\sim10.5$ where
the main sequence starts bending, we find tantalising 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,
$\lambda_{Re}$ remains roughly constant and only at very high stellar masses
($\log M_{\star}[\rm{M}_{\odot}]>11$), do we see a rapid decrease in
$\lambda_{Re}$ 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 while 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 $z\sim0$.
