Location fingerprinting based on RSSI becomes a mainstream indoor localization technique due to its advantage of not requiring the installation of new infrastructure and the modification of existing devices, especially given the prevalence of Wi-Fi-enabled devices and the ubiquitous Wi-Fi access in modern buildings. The use of AI/ML technologies like DNNs makes location fingerprinting more accurate and reliable, especially for large-scale multi-building and multi-floor indoor localization. The application of DNNs for indoor localization, however, depends on a large amount of preprocessed and deliberately-labeled data for their training. Considering the difficulty of the data collection in an indoor environment, especially under the current epidemic situation of COVID-19, we investigate three different methods of RSSI data augmentation based on Multi-Output Gaussian Process (MOGP), i.e., by a single floor, by neighboring floors, and by a single building; unlike Single-Output Gaussian Process (SOGP), MOGP can take into account the correlation among RSSI observations from multiple Access Points (APs) deployed closely to each other (e.g., APs on the same floor of a building) by collectively handling them. The feasibility of the MOGP-based RSSI data augmentation is demonstrated through experiments based on the state-of-the-art RNN indoor localization model and the UJIIndoorLoc, i.e., the most popular publicly-available multi-building and multi-floor indoor localization database, where the RNN model trained with the UJIIndoorLoc database augmented by using the whole RSSI data of a building in fitting an MOGP model (i.e., by a single building) outperforms the other two augmentation methods as well as the RNN model trained with the original UJIIndoorLoc database, resulting in the mean three-dimensional positioning error of 8.42 m.