Semi-supervised domain adaptation (SSDA) aims at training a high-performance model for a target domain using few labeled target data, many unlabeled target data, and plenty of auxiliary data from a source domain. Previous works in SSDA mainly focused on learning transferable representations across domains. However, it is difficult to find a feature space where the source and target domains share the same conditional probability distribution. Additionally, there is no flexible and effective strategy extending existing unsupervised domain adaptation (UDA) approaches to SSDA settings. In order to solve the above two challenges, we propose a novel fine-tuning framework, semi-supervised transfer boosting (SS-TrBoosting). Given a well-trained deep learning-based UDA or SSDA model, we use it as the initial model, generate additional base learners by boosting, and then use all of them as an ensemble. More specifically, half of the base learners are generated by supervised domain adaptation, and half by semi-supervised learning. Furthermore, for more efficient data transmission and better data privacy protection, we propose a source data generation approach to extend SS-TrBoosting to semi-supervised source-free domain adaptation (SS-SFDA). Extensive experiments showed that SS-TrBoosting can be applied to a variety of existing UDA, SSDA and SFDA approaches to further improve their performance.