How to structure completely different workflows needs

Hello,

We are a small company expanding additional departments into using Zendesk. A new department we want to add has VERY different time expectations on responses and "resolution" times. I was thinking that using a unique form would be a good start. In addition to that, since the triggers / automatons would be different in nature, is it easier to add them to our existing 1 "brand" (where everything else is) OR to create a new "brand" (even though it's a department) and set everything up through that way and keep them separate? My once issue with this ladder approach is that sometimes questions related to that department may come in at the primary customer service location - would they be able to transfer a ticket to another "brand"?

I'm open to ideas! Thanks.