Major trade-offs often manifest as axes of diversity in organismal functional systems. Overarching trade-offs may result in high trait integration and restrict the trajectory of diversification to be along a single axis. Here, we explore the diversification of the feeding mechanism in coral reef fishes to establish the role of trade-offs and complexity in a spectacular ecological radiation. We show that the primary axis of variation in the measured musculo-skeletal traits is aligned with a trade-off between mobility and force transmission, spanning species that capture prey with suction and those that bite attached prey. We found weak or no covariation between about half the traits, reflecting deviations from the trade-off axis. The dramatic trophic range found among reef fishes occurs along the primary trade-off axis, with numerous departures that use a mosaic of trait combinations to adapt the feeding mechanism to diverse challenges. We suggest that morphological evolution both along and independent of a major axis of variation is a widespread mechanism of diversification in complex systems where a global trade-off shapes major patterns of diversity. Significant additional diversity emerges as systems use weak integration and complexity to assemble functional units with many trait combinations that meet varying ecological demands.