A brief overview is given of recent developments and fresh ideas at the intersection of PT-and/or CPT-symmetric quantum mechanics with supersymmetric quantum mechanics (SUSY QM). Within the framework of the resulting supersymmetric version of CPT-symmetric quantum mechanics we study the consequences of the assumption that the "charge" operator C is represented in a, differential-operator form of the second or higher order. Besides the freedom allowed by the Hermiticity constraint for the operator CP, encouraging results are obtained in the second-order case. In particular, the integrability of intertwining relations proves to match the closure of our nonlinear (viz., polynomial) SUSY algebra. In a particular illustration, our form of CPT-symmetric SUSY QM leads to a new class of non-Hermitian polynomial oscillators with real spectrum which turn out to be PT-asymmetric. © World Scientific Publishing Company.