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In a previous work, we have identified the spin of the dominant black hole of a binary from its jet properties. Analysing Very Long Baseline Array (VLBA) observations of the quasar S5 1928+738, taken at 15-GHz during 43 epochs between 1995.96 and 2013.06, we showed that the inclination angle variation of the inner (<2 mas) jet symmetry axis naturally decomposes into a periodic and a monotonic contribution. The former emerges due to the Keplerian orbital evolution, while the latter is interpreted as the signature of the spin-orbit precession of the jet emitting black hole. In this paper, we revisit the analysis of the quasar S5 1928+738 by including new 15-GHz VLBA observations extending over 29 additional epochs, between 2013.34 and 2020.89. The extended data set confirms our previous findings which are further supported by the flux density variation of the jet. By applying an enhanced jet precession model that can handle arbitrary spin orientations κ with respect to the orbital angular momentum of a binary supermassive black hole system, we estimate the binary mass ratio as ν = 0.21 ± 0.04 for κ = 0 (i.e. when the spin direction is perpendicular to the orbital plane) and as ν = 0.32 ± 0.07 for κ = π/2 (i.e. when the spin lies in the orbital plane). We estimate more precisely the spin precession velocity, halving its uncertainty from $(-0.05\pm 0.02)$ to $(-0.04\pm 0.01)^{\circ }\, \mathrm{yr}^{-1}$.