We approach the challenge of addressing semi-supervised domain generalization (SSDG). Specifically, our aim is to obtain a model that learns domain-generalizable features by leveraging a limited subset of labelled data alongside a substantially larger pool of unlabeled data. Existing domain generalization (DG) methods which are unable to exploit unlabelled data perform poorly compared to semi-supervised learning (SSL) methods under SSDG setting. Nevertheless, SSL methods have a considerable room for performance improvement when compared to fully-supervised DG training. To tackle this underexplored, yet highly practical problem of SSDG, we make the following core contributions. First, we propose a feature-based conformity technique that matches the posterior distributions from the feature space with the pseudo-label from the model's output space. Second, we develop a semantics alignment loss to learn semantically-compatible representations by regularizing the semantic structure in the feature space. Our method is plug-and-play and can be readily integrated with different SSL-based SSDG baselines without introducing any additional parameters. Extensive experimental results across five challenging DG benchmarks with four strong SSL baselines suggest that our method provides consistent and notable gains in two different SSDG settings. Our code will be made publicly available.