The planetary boundaries framework defines a safe operating space for humanity. To date, these boundaries have mostly been investigated separately, and it is unclear whether breaching one boundary can lead to the transgression of another. By employing a dynamic global vegetation model, we systematically simulate the strength and direction of the effects of different transgression levels of the climate change boundary (using climate output from ten phase 6 of the Coupled Model Intercomparison Project models for CO₂ levels ranging from 350 ppm to 1000 ppm). We focus on climate change-induced shifts of Earth's major forest biomes, the control variable for the land-system change boundary, both by the end of this century and, to account for the long-term legacy effect, by the end of the millennium. Our simulations show that while staying within the 350 ppm climate change boundary co-stabilizes the land-system change boundary, breaching it (>450 ppm) leads to critical transgression of the latter, with greater severity the higher the ppm level rises and the more time passes. Specifically, this involves a poleward treeline shift, boreal forest dieback (nearly completely within its current area under extreme climate scenarios), competitive expansion of temperate forest into today's boreal zone, and a slight tropical forest extension. These interacting changes also affect other planetary boundaries (freshwater change and biosphere integrity) and provide feedback to the climate change boundary itself. Our quantitative process-based study highlights the need for interactions to be studied for a systemic operationalization of the planetary boundaries framework.