Wi-Fi fingerprinting becomes a dominant solution for large-scale indoor localization due to its major advantage of not requiring new infrastructure and dedicated devices. The number and the distribution of Reference Points (RPs) for the measurement of localization fingerprints like RSSI during the offline phase, however, greatly affects the localization accuracy; for instance, the UJIIndoorLoc is known to have the issue of uneven spatial distribution of RPs over buildings and floors. Data augmentation has been proposed as a feasible solution to not only improve the smaller number and the uneven distribution of RPs in the existing fingerprint databases but also reduce the labor and time costs of constructing new fingerprint databases. In this paper, we propose the multidimensional augmentation of fingerprint data for indoor localization in a large-scale building complex based on Multi-Output Gaussian Process (MOGP) and systematically investigate the impact of augmentation ratio as well as MOGP kernel functions and models with their hyperparameters on the performance of indoor localization using the UJIIndoorLoc database and the state-of-the-art neural network indoor localization model based on a hierarchical RNN. The investigation based on experimental results suggests that we can generate synthetic RSSI fingerprint data up to ten times the original data -- i.e., the augmentation ratio of 10 -- through the proposed multidimensional MOGP-based data augmentation without significantly affecting the indoor localization performance compared to that of the original data alone, which extends the spatial coverage of the combined RPs and thereby could improve the localization performance at the locations that are not part of the test dataset.