Parameters can only accept a single value, not multiple values.
From the sounds of it, a parameter may not be your best option, but rather a quick filter showing the users. Then, the department quick filter would show Only Relevant Values, based on what is selected in the User quick filter. The following link describes Only Relevant Values:
Hope this helps!
I am sure this is a common request but are there plans in place to develop dashboard level filters. I am often using multiple datasets in my models, where without care and attention you can believe you are looking at the same time periods when infact they vary as each has to be controlled by a quick filter.
I love Tableau, but have used Omniscope from Visokio for 6 years and find their dashboard approach much more intuitive in this respect.