Although the landscape for treating acute myeloid leukemia (AML) patients has changed substantially in recent years, the majority of patients will eventually relapse and succumb to their disease. Allogeneic stem cell transplantation provides the best anti-AML treatment strategy, but is only suitable in a minority of patients. In contrast to B-cell neoplasias, chimeric antigen receptor (CAR) T-cell therapy in AML has encountered challenges in target antigen heterogeneity, safety, and T-cell dysfunction. We established a Fab-based adapter CAR (AdCAR) T-cell platform with flexibility of targeting and control of AdCAR T-cell activation. Utilizing AML cell lines and a long-term culture assay for primary AML cells, we were able to demonstrate AML-specific cytotoxicity using anti-CD33, anti-CD123, and anti-CLL1 adapter molecules in vitro and in vivo. Notably, we show for the first time the feasibility of sequential application of adapter molecules of different specificity in primary AML co-cultures. Importantly, using the AML platform, we were able to demonstrate that chronic T-cell stimulation and exhaustion can be counteracted through introduction of treatment-free intervals. As T-cell exhaustion and target antigen heterogeneity are well-known causes of resistance, the AdCAR platform might offer effective strategies to ameliorate these limitations.