While advances in foundation models have extended to the time series domain, they have primarily focused on designing model architectures to address external heterogeneity between datasets, e.g., varying numbers of channels, often overlooking internal heterogeneity, e.g., varying channel dependencies. In this paper, we introduce the concept of partial channel dependence (PCD) to partially adjust the channel dependency based on dataset-specific information. To achieve PCD, we propose a channel masking strategy that captures the relationships between channels within a dataset by a correlation matrix encoding relative dependencies between channels and domain parameters learning the absolute dependencies specific to each dataset. We validate the effectiveness of our method across various tasks, including forecasting, classification, imputation, and anomaly detection.