Classifying patterns of known classes and rejecting ambiguous and novel (also called as out-of-distribution (OOD)) inputs are involved in open world pattern recognition. Deep neural network models usually excel in closed-set classification while performs poorly in rejecting OOD inputs. To tackle this problem, numerous methods have been designed to perform open set recognition (OSR) or OOD rejection/detection tasks. Previous methods mostly take post-training score transformation or hybrid models to ensure low scores on OOD inputs while separating known classes. In this paper, we attempt to build a unified framework for building open set classifiers for both classification and OOD rejection. We formulate the open set recognition of $ K $-known-class as a $ (K+1) $-class classification problem with model trained on known-class samples only. By decomposing the $ K $-class problem into $ K $ one-versus-all (OVA) binary classification tasks and binding some parameters, we show that combining the scores of OVA classifiers can give $ (K+1) $-class posterior probabilities, which enables classification and OOD rejection in a unified framework. To maintain the closed-set classification accuracy of the OVA trained classifier, we propose a hybrid training strategy combining OVA loss and multi-class cross-entropy loss. We implement the OVA framework and hybrid training strategy on the recently proposed convolutional prototype network and prototype classifier on vision transformer (ViT) backbone. Experiments on popular OSR and OOD detection datasets demonstrate that the proposed framework, using a single multi-class classifier, yields competitive performance in closed-set classification, OOD detection, and misclassification detection.