A soft sensor concept is typically developed and calibrated for individual bioprocesses in a time-consuming manual procedure. Following that, the prediction performance of these soft sensors degrades over time, due to changes in raw materials, biological variability, and modified process strategies. Through automatic adaptation and recalibration, adaptive soft sensor concepts have the potential to generalize soft sensor principles and make them applicable across bioprocesses. In this study, a new generalized adaptation algorithm for soft sensors is developed to provide phase-dependent recalibration of soft sensors based on multiway principal component analysis, a similarity analysis, and robust, generalist phase detection in multiphase bioprocesses. This generalist soft sensor concept was evaluated in two multiphase bioprocesses with various target values, media, and microorganisms. Consequently, the soft sensor concept was tested for biomass prediction in a Pichia pastoris process, and biomass and protein prediction in a Bacillus subtilis process, where the process characteristics (cultivation media and cultivation strategy) were varied. High prediction performance was demonstrated for P. pastoris processes (relative error = 6.9%) as well as B. subtilis processes in two different media during batch and fed-batch phases (relative errors in optimized high-performance medium: biomass prediction = 12.2%, protein prediction = 7.2%; relative errors in standard medium: biomass prediction = 12.8%, protein prediction = 8.8%).