Domain shift, the mismatch between training and testing data characteristics, causes significant degradation in the predictive performance in multi-source imaging scenarios. In medical imaging, the heterogeneity of population, scanners and acquisition protocols at different sites presents a significant domain shift challenge and has limited the widespread clinical adoption of machine learning models. Harmonization methods, which aim to learn a representation of data invariant to these differences are the prevalent tools to address domain shift, but they typically result in degradation of predictive accuracy. This paper takes a different perspective of the problem: we embrace this disharmony in data and design a simple but effective framework for tackling domain shift. The key idea, based on our theoretical arguments, is to build a pretrained classifier on the source data and adapt this model to new data. The classifier can be fine-tuned for intra-study domain adaptation. We can also tackle situations where we do not have access to ground-truth labels on target data; we show how one can use auxiliary tasks for adaptation; these tasks employ covariates such as age, gender and race which are easy to obtain but nevertheless correlated to the main task. We demonstrate substantial improvements in both intra-study domain adaptation and inter-study domain generalization on large-scale real-world 3D brain MRI datasets for classifying Alzheimer’s disease and schizophrenia.