Increased maintenance costs at cellular, and consequently organism level, are thought to be involved in shaping the sensitivity of marine calcifiers to ocean acidification (OA). Yet, knowledge of the capacity of marine calcifiers to undergo metabolic adaptation is sparse. In Kiel Fjord, blue mussels thrive despite periodically high seawater PCO2, making this population interesting for studying metabolic adaptation under OA. Consequently, we conducted a multi-generation experiment and compared physiological responses of F1 mussels from `tolerant' and `sensitive' families exposed to OA for 1 year. Family classifications were based on larval survival; tolerant families settled at all PCO2 levels (700, 1120, 2400 {\textmu}atm) while sensitive families did not settle at the highest PCO2 (≥99.8{%} mortality). We found similar filtration rates between family types at the control and intermediate PCO2 level. However, at 2400 {\textmu}atm, filtration and metabolic scope of gill tissue decreased in tolerant families, indicating functional limitations at the tissue level. Routine metabolic rates (RMR) and summed tissue respiration (gill and outer mantle tissue) of tolerant families were increased at intermediate PCO2, indicating elevated cellular homeostatic costs in various tissues. By contrast, OA did not affect tissue and routine metabolism of sensitive families. However, tolerant mussels were characterised by lower RMR at control PCO2 than sensitive families, which had variable RMR. This might provide the energetic scope to cover increased energetic demands under OA, highlighting the importance of analysing intra-population variability. The mechanisms shaping such difference in RMR and scope, and thus species' adaptation potential, remain to be identified.