Summary Its features as a microbial and eukaryotic organism have turned Komagataella phaffii (Pichia pastoris) into an emerging cell factory for recombinant protein production (RPP). As a key step of the bioprocess development, this work aimed to demonstrate the importance of tailor designing the cultivation strategy according to the production kinetics of the cell factory. For this purpose, K. phaffii clones constitutively expressing (PGAP) Candida rugosa lipase 1 (Crl1) with different gene dosage were used as models in continuous and fed‐batch cultures. Production parameters were much greater with a multicopy clone (MCC) than with the single‐copy clone (SCC). Regarding production kinetics, the specific product generation rate (qP) increased linearly with increasing specific growth rate (µ) in SCC; by contrast, qP exhibited saturation in MCC. A transcriptional analysis in chemostat cultures suggested the presence of eventual post‐transcriptional bottlenecks in MCC. After the strain characterization, in order to fulfil overall development of the bioprocess, the performance of both clones was also evaluated in fed‐batch mode. Strikingly, different optimal strategies were determined for both models due to the different production kinetic patterns observed as a trade‐off for product titre, yields and productivity. The combined effect of gene dosage and adequate µ enables rational process development with a view to optimize K. phaffii RPP bioprocesses.