We use Kanban for several departments because our Tool Zenkit is not only a Kanban Board. You can work with multiple data views, for example, a Calendar.
In Marketing, we use it for task management. Prioritization can be used via due dates, the order of the items or by setting labels with "high", "medium" or "low". We add almost everything to the board to have a good overview of the workload or we add checklists to an item where we can see what to do within this task.
Everyone can move his items to "Done" and I get informed or we use the column "need confirmation" to check if the task is all done. And with the Calendar view, a team calendar isn´t a problem anymore.
More Infos about Zenkit: https://zenkit.com