Metabolic rates are fundamental to many biological processes, and commonly scale with body size with an exponent (bR) between 2/3 and 1 for reasons still debated. According to the ‘metabolic-level boundaries hypothesis',bRdepends on the metabolic level (LR). We test this prediction and show that across cephalopod species intraspecificbRcorrelates positively with not onlyLRbut also the scaling of body surface area with body mass. Cephalopod species with highLRmaintain near constant mass-specific metabolic rates, growth and probably inner-mantle surface area for exchange of respiratory gases or wastes throughout their lives. By contrast, teleost fish show a negative correlation betweenbRandLR. We hypothesize that this striking taxonomic difference arises because both resource supply and demand scale differently in fish and cephalopods, as a result of contrasting mortality and energetic pressures, likely related to different locomotion costs and predation pressure. Cephalopods with highLRexhibit relatively steep scaling of growth, locomotion, and resource-exchange surface area, made possible by body-shape shifting. We suggest that differences in lifestyle, growth and body shape with changing water depth may be useful for predicting contrasting metabolic scaling for coexisting animals of similar sizes.This article is part of the theme issue ‘Physiological diversity, biodiversity patterns and global climate change: testing key hypotheses involving temperature and oxygen’.