mansion, large building, palace
舘 centers on a grand, imposing structure: a mansion, large building, or palace. It conveys a sense of official or stately residence.
舘 combines 舍 (building, inn) and 官 (official, government), suggesting an official residence or large building. The exact historical development is uncertain, but the component combination fits the meaning well.
The left side 舍 looks like a building with a roof, and the right side 官 suggests an official. Picture an official's grand mansion with a distinctive roof.
For カン, imagine a can of paint being used to touch up the grand mansion: can -> カン, and the official building gets a fresh coat.