Scientific management of ecosystems to enhance the sustainable supply of multiple ecosystem services (ES) is important for regional high-quality development. The precise formulation of ecosystem management measures requires a deeper understanding of the interaction effects between multiple drivers of ES and their key impact thresholds, yet current research has limited understanding of this problem. This study took the Yangtze River Delta (YRD) region in 2020 as an example and assessed the supply of 6 key ES (Climate Regulation, Carbon Sequestration, Soil Retention, Water Yield, Food Production, Leisure and Recreation) in 2020 by using models such as InVEST, CASA, and MaxENT. The constraint line method was used to analyze the constraining effect of the single driver on each ES and its key thresholds. Furthermore, the study revealed the interactive effects of multiple drivers and their impact thresholds by using conditional inference trees. The study results showed that: (1) The 6 ES in the YRD were characterized by remarkable spatial heterogeneity and are affected by 12 ecological-socioeconomic drivers, among which climate and land use were the most significant. (2) The 12 drivers showed 4 non-linear and 2 linear patterns for the 6 ES, with 32 key impact thresholds. (3) Specific ecological drivers significantly affected ES within the thresholds formed by multi-factor interactions, for example, solar radiation significantly increased water production in the condition consisting of the specific combination of rainfall (1604.6 mm—1808.5mm) and wind speed (4.3m/s—4.8m/s). The study innovatively integrates the constraint lines and conditional inference trees to reveal the nonlinear effects of the driving factors and their key impact thresholds, which provides methodological reference and decision-making basis for the formulation of ecosystem management measures in the YRD.