We report the fabrication of polymersomes, using as building blocks star-graft quarterpolymers, composed of hydrophobic polystyrene and pH-sensitive poly(2-vinylpyridine)-b-poly(acrylic acid) (P2VP-b-PAA) arms, emanated from a common nodule, enriched by thermosensitive poly(N-isopropylacrylamide) grafts covalently bonded on the PAA block-arms. These multicompartmental polymersomes were evaluated as nanocarriers for the encapsulation and controlled co-delivery of doxorubicin (hydrophilic) and paclitaxel (hydrophobic) chemotherapeutic agents. The polymersomes can load these drugs in different compartments and can efficiently be internalized in the human lung adenocarcinoma epithelial cells, delivering their cargo and inducing high cell apoptosis. The release kinetics of both anticancer agents was controlled differently by the environmental conditions (pH and temperature). Enhanced release was observed at the acidic pH 6.0 and under physiological temperature (37 °C). At the same total drug level, co-delivery of these drugs with the polymersomes caused enhanced cytotoxicity and induced significantly higher cell apoptosis in the cancer cell line compared to the polymersomes loaded with either of the two drugs.