The large spread of online shopping has led computer vision researchers to develop different solutions for the fashion domain to potentially increase the online user experience and improve the efficiency of preparing fashion catalogs. Among them, image-based virtual try-on has recently attracted a lot of attention resulting in several architectures that can generate a new image of a person wearing an input try-on garment in a plausible and realistic way. In this paper, we present VITON-GT, a new model for virtual try-on that generates high-quality and photo-realistic images thanks to multiple geometric transformations. In particular, our model is composed of a two-stage geometric transformation module that performs two different projections on the input garment, and a transformation-guided try-on module that synthesize the new image. We experimentally validate the proposed solution on the most common dataset for this task, containing mainly t-shirts, and we demonstrate its effectiveness compared to different baselines and previous methods. Additionally, we assess the generalization capabilities of our model on a new set of fashion items composed of upper-body clothes from different categories. To the best of our knowledge, we are the first to test virtual try-on architectures in this challenging experimental setting.