© 2016 The Authors. We report an expanded sample of visual morphological classifications from the Galaxy and Mass Assembly survey phase two, which now includes 7556 objects (previously 3727 in phase one). We define a local (z <0.06) sample and classify galaxies into E, S0-Sa, SB0-SBa, Sab- Scd, SBab-SBcd, Sd-Irr, and 'little blue spheroid' types. Using these updated classifications, we derive stellar mass function fits to individual galaxy populations divided both by morphological class and more general spheroid- or disc-dominated categories with a lower mass limit of log(M*/M?) = 8 (one dex below earlier morphological mass function determinations). We find that all individual morphological classes and the combined spheroid-/bulge-dominated classes are well described by single Schechter stellarmass function forms. We find that the total stellar mass densities for individual galaxy populations and for the entire galaxy population are bounded within our stellar mass limits and derive an estimated total stellar mass density of ?* = 2.5 × 108 M? Mpc-3 h0.7, which corresponds to an approximately 4 per cent fraction of baryons found in stars. The mass contributions to this total stellar mass density by galaxies that are dominated by spheroidal components (E and S0-Sa classes) and by disc components (Sab-Scd and Sd-Irr classes) are approximately 70 and 30 per cent, respectively.