Inspired by the observations of three P c states, we systematically investigate interactions between an S-wave charmed baryon B (*) c = c / c / * c and an anticharmed mesonT =D 1 /D * 2 with the one-pion-exchange potential model and the one-boson-exchange potential model, and search for possible new types of P c states with the structures of B (*) cT. Both S-D wave mixing and coupled channel effects are considered. Our results suggest that in some B (*) cT systems there are ideal candidates of new types of P c states-i.e., the cD1 state with I (J P) = 1/2(1/2 +), the cD * 2 state with I (J P) = 1/2(3/2 +), the * cD 1 state with I (J P) = 1/2(1/2 +), and the * cD * 2 states with I (J P) = 1/2(1/2 + , 3/2 +)-and we suggest that these predicted new types of P c states can be detected in the process 0 b → ψ (2S)pπ −. Meanwhile, we also extend our study to the interactions between an S-wave charmed baryon and a charmed meson in a T doublet, and we predict a series of double-charm molecular pentaquarks.