Production of heterologous proteins in Pichia pastoris (syn. Komagataella sp.) has been shown to exert a metabolic burden on the host metabolism. This burden is associated with metabolite drain, which redirects nucleotides and amino acids from primary metabolism. On the other hand, recombinant protein production affects energy and redox homeostasis of the host cell. In a previous study, we have demonstrated that overexpression of single genes of the oxidative pentose phosphate pathway (PPP) had a positive influence on recombinant production of cytosolic human superoxide dismutase (hSOD). In this study, different combinations of these genes belonging to the oxidative PPP were generated and analyzed. Thereby, a 3.8-fold increase of hSOD production was detected when glucose-6-phosphate dehydrogenase (ZWF1) and 6-gluconolactonase (SOL3) were simultaneously overexpressed, while the combinations of other genes from PPP had no positive effect on protein production. By measuring isotopologue patterns of 13C-labelled metabolites, we could detect an upshift in the flux ratio of PPP to glycolysis upon ZWF1 and SOL3 co-overexpression, as well as increased levels of 6-phosphogluconate. The substantial improvement of hSOD production by ZWF1 and SOL3 co-overexpression appeared to be connected to an increase in PPP flux. In conclusion, we show that overexpression of SOL3 together with ZWF1 enhanced both the PPP flux ratio and hSOD accumulation, providing evidence that in P. pastoris Sol3 limits the flux through PPP and recombinant protein production.