Chimeric antigen receptor (CAR) T cell therapies are medical breakthroughs in cancer treatment. However, treatment failure is often caused by CAR T cell dysfunction. Additional approaches are needed to overcome inhibitory signals that limit anti-tumor potency. Here, we developed bifunctional fusion "degrader" proteins that bridge one or more target proteins and an E3 ligase complex to enforce target ubiquitination and degradation. Conditional degradation strategies were developed using inducible degrader transgene expression or small molecule-dependent E3 recruitment. We further engineered degraders to block SMAD-dependent TGFβ signaling using a domain from the SARA protein to target both SMAD2 and SMAD3. SMAD degrader CAR T cells were less susceptible to suppression by TGFβ and demonstrated enhanced anti-tumor potency in vivo. These results demonstrate a clinically suitable synthetic biology platform to reprogram E3 ligase target specificity for conditional, multi-specific endogenous protein degradation, with promising applications including enhancing the potency of CAR T cell therapy.