Rare gastrointestinal stromal tumors (GISTs) are caused by mutations in the KIT and PDGFRA genes. Avapritinib (BLU-285) is a targeted selective inhibitor for mutated KIT and PDGFRA receptors that can be used to treat these tumors. However, there are subtypes of GISTs that exhibit resistance against BLU-285 and thus require other treatment strategies. This can be addressed by employing a drug delivery system that transports a combination of drugs with distinct cell targets. In this work, we present the synthesis of esterase-responsive polyglycerol-based nanogels (NGs) to overcome drug resistance in rare GISTs. Using inverse nanoprecipitation mediated with inverse electron-demand Diels-Alder cyclizations (iEDDA) between dPG-methyl tetrazine and dPG-norbornene, multi-drug-loaded NGs were formed based on a surfactant-free encapsulation protocol. The obtained NGs displayed great stability in the presence of fetal bovine serum (FBS) and did not trigger hemolysis in red blood cells over a period of 24 h. Exposing the NGs to Candida Antarctica Lipase B (CALB) led to the degradation of the NG network, indicating the capability of targeted drug release. The bioactivity of the loaded NGs was tested in vitro on various cell lines of the GIST-T1 family, which exhibit different drug resistances. Cell internalization with comparable uptake kinetics of the NGs could be confirmed by confocal laser scanning microscopy (CLSM) and flow cytometry for all cell lines. Cell viability and live cell imaging studies revealed that the loaded NGs are capable of intracellular drug release by showing similar IC50 values to those of the free drugs. Furthermore, multi-drug-loaded NGs were capable of overcoming BLU-285 resistance in T1-α-D842V + G680R cells, demonstrating the utility of this carrier system.