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In medical imaging, organ/pathology segmentation models trained on current publicly available and fully-annotated datasets usually do not well-represent the heterogeneous modalities, phases, pathologies, and clinical scenarios encountered in real environments. On the other hand, there are tremendous amounts of unlabelled patient imaging scans stored by many modern clinical centers. In this work, we present a novel segmentation strategy, co-heterogenous and adaptive segmentation (CHASe), which only requires a small labeled cohort of single phase imaging data to adapt to any unlabeled cohort of heterogenous multi-phase data with possibly new clinical scenarios and pathologies. To do this, we propose a versatile framework that fuses appearance based semi-supervision, mask based adversarial domain adaptation, and pseudo-labeling. We also introduce co-heterogeneous training, which is a novel integration of co-training and hetero modality learning. We have evaluated CHASe using a clinically comprehensive and challenging dataset of multi-phase computed tomography (CT) imaging studies (1147 patients and 4577 3D volumes). Compared to previous state-of-the-art baselines, CHASe can further improve pathological liver mask Dice-Sorensen coefficients by ranges of $4.2\% \sim 9.4\%$, depending on the phase combinations: e.g., from $84.6\%$ to $94.0\%$ on non-contrast CTs.