We introduce a new Monte Carlo based method to evaluate American options under parameter uncertainty within a multifactor framework. The classical approach, referred to as the Longstaff-Schwartz Monte Carlo method, cannot deal with such a setup. Our proposed method, therefore, provides a significant extension of the computational toolbox relevant to American options and optimal stopping problems. We first reformulate the underlying American option price as the solution of a reflected backward stochastic differential equation (RBSDE) with a uniformly Lipschitz continuous generator and propose an algorithm based on stratified sampling. The proposed algorithm allows parallelization on graphics processing units (GPUs), and provides accurate and computationally efficient estimates of option prices under different multifactor models. Through extensive numerical experiments using calibrated models, we demonstrate the convergence of the proposed scheme. Finally, using our algorithm, we quantify the loss of premium due to parameter uncertainty for financial options, which can be useful when looking at the impact of model calibration error.