How do I create a few standard competencies or tasks that would address the needs of multiple business units?

The most important thing to remember about competency models is that for them to be effective, they must be relevant. A competency model describes what each person in their role needs to be able to do, specifically, in order to perform their part of corporate strategy. If they are too generic, they will no longer be effective.

Additionally, if you want to use them for career planning, they must be differentiated.  You need to be able to try on other jobs for size and see how they fit.  If all roles have the same competencies, and nothing is role-based, this is not possible.

That being said, there are some competencies or tasks that can be shared across roles and business units, including those required for the future of work. Examples include: data analysis, dealing with ambiguity and change, learning agility, influencing, and collaboration.