The fuel economy (FE) of the parallel hybrid electric vehicle (HEV) suffers due to significant energy losses from the wet clutches of the automatic transmission and limited engine operations. To overcome these limitations, a novel clutchless multimode parallel HEV (CMP-HEV) was proposed previously, but its operational feasibility was not proven. In this study, we propose a systematic methodology that can assess the feasibility of the CMP-HEV and efficiently optimize FE and acceleration performance of the design, simultaneously. Using the dynamic models, we assess the feasibility over the entire design spaces under two conditions: full acceleration (for drivability) and moderate acceleration (for fuel efficiency). An instantaneous optimization method is used to rapidly evaluate the full acceleration performance, and the designs with poor acceleration are considered infeasible. For the fuel efficiency, the feasibility is determined by the violation of electric motor constraints under the assumption of efficient engine operations. The feasible design sets from the assessment are used for the design optimization. Dynamic programming is applied over only the feasible design space, and the Pareto front is obtained to show the tradeoff between FE and acceleration performance. The selected final design is found superior to a comparable parallel HEV in both FE and acceleration performance perspectives.