Phytoplankton growth is controlled by multiple environmental drivers, which are all modified by climate change. While numerous experimental studies identify interactive effects between drivers, large-scale ocean biogeochemistry models mostly account for growth responses to each driver separately and leave the results of these experimental multiple-driver studies largely unused. Here, we amend phytoplankton growth functions in a biogeochemical model by dual-driver interactions (CO2 and temperature, CO2 and light), based on data of a published meta-analysis on multiple-driver laboratory experiments. The effect of this parametrization on phytoplankton biomass and community composition is tested using present-day and future high-emission (SSP5-8.5) climate forcing. While the projected decrease in future total global phytoplankton biomass in simulations with driver interactions is similar to that in control simulations without driver interactions (5%-6%), interactive driver effects are group-specific. Globally, diatom biomass decreases more with interactive effects compared with the control simulation (-8.1% with interactions vs. no change without interactions). Small-phytoplankton biomass, by contrast, decreases less with on-going climate change when the model accounts for driver interactions (-5.0% vs. -9.0%). The response of global coccolithophore biomass to future climate conditions is even reversed when interactions are considered (+33.2% instead of -10.8%). Regionally, the largest difference in the future phytoplankton community composition between the simulations with and without driver interactions is detected in the Southern Ocean, where diatom biomass decreases (-7.5%) instead of increases (+14.5%), raising the share of small phytoplankton and coccolithophores of total phytoplankton biomass. Hence, interactive effects impact the phytoplankton community structure and related biogeochemical fluxes in a future ocean. Our approach is a first step to integrate the mechanistic understanding of interacting driver effects on phytoplankton growth gained by numerous laboratory experiments into a global ocean biogeochemistry model, aiming toward more realistic future projections of phytoplankton biomass and community composition.