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Deep neural networks suffer from significant performance deterioration when there exists distribution shift between deployment and training. Domain Generalization (DG) aims to safely transfer a model to unseen target domains by only relying on a set of source domains. Although various DG approaches have been proposed, a recent study named DomainBed, reveals that most of them do not beat the simple Empirical Risk Minimization (ERM). To this end, we propose a general framework that is orthogonal to existing DG algorithms and could improve their performance consistently. Unlike previous DG works that stake on a static source model to be hopefully a universal one, our proposed AdaODM adaptively modifies the source model at test time for different target domains. Specifically, we create multiple domain-specific classifiers upon a shared domain-generic feature extractor. The feature extractor and classifiers are trained in an adversarial way, where the feature extractor embeds the input samples into a domain-invariant space, and the multiple classifiers capture the distinct decision boundaries that each of them relates to a specific source domain. During testing, distribution differences between target and source domains could be effectively measured by leveraging prediction disagreement among source classifiers. By fine-tuning source models to minimize the disagreement at test time, target domain features are well aligned to the invariant feature space. We verify AdaODM on two popular DG methods, namely ERM and CORAL, and four DG benchmarks, namely VLCS, PACS, OfficeHome, and TerraIncognita. The results show AdaODM stably improves the generalization capacity on unseen domains and achieves state-of-the-art performance.