In recent years, numerous screening methods have been published for ultrahigh-dimensional data that contain hundreds of thousands of features; however, most of these features cannot handle data with thousands of classes. Prediction models built to authenticate users based on multichannel biometric data result in this type of problem. In this study, we present a novel method known as random forest-based multiround screening (RFMS) that can be effectively applied under such circumstances. The proposed algorithm divides the feature space into small subsets and executes a series of partial model builds. These partial models are used to implement tournament-based sorting and the selection of features based on their importance. To benchmark RFMS, a synthetic biometric feature space generator known as BiometricBlender is employed. Based on the results, the RFMS is on par with industry-standard feature screening methods while simultaneously possessing many advantages over these methods.