Nowadays, cloud-based services are widely favored over the traditional approach of locally training a Neural Network (NN) model. Oftentimes, a cloud service processes multiple requests from users--thus training multiple NN models concurrently. However, training NN models concurrently is a challenging process, which typically requires significant amounts of available computing resources and takes a long time to complete. In this paper, we present UnifiedNN to effectively train multiple NN models concurrently on the cloud. UnifiedNN effectively "combines" multiple NN models and features several memory and time conservation mechanisms to train multiple NN models simultaneously without impacting the accuracy of the training process. Specifically, UnifiedNN merges multiple NN models and creates a large singular unified model in order to efficiently train all models at once. We have implemented a prototype of UnifiedNN in PyTorch and we have compared its performance with relevant state-of-the-art frameworks. Our experimental results demonstrate that UnifiedNN can reduce memory consumption by up to 53% and training time by up to 81% when compared with vanilla PyTorch without impacting the model training and testing accuracy. Finally, our results indicate that UnifiedNN can reduce memory consumption by up to 52% and training time by up to 41% when compared to state-of-the-art frameworks when training multiple models concurrently.