Cost Center approval based on Project Org

Content

We are a higher education institution that uses a lot of grants/awards. With current workflow configuration, we have approvals always going to the Cost Center whether it belongs to the employee submitting or not. We always want the Cost Center to receive approvals for expenses. We also have the PI approval turned on for any project related transaction. What I'd like to accomplish is to have the Cost Center for the Project Owning Org receive approval when a project is used rather than the employee default Cost Center. 

Example of current workflow:
I work in English and am submitting an expense report. My default org is 21003 so my Cost Center approval goes to Regina. I'm using a project, so project approval goes to David (the PI). The project owning organization is Chemistry and not English, but the Chemistry approver does not receive approval. The only way for Chemistry to be included is if the employee knows and manually updates the org to 21099 to reflect Chemistry.