There is really no simple answer but I would start by clearly defining roles on who is responsible for priorities, who is responsible for facilitating the prior

There is really no simple answer but I would start by clearly defining roles on who is responsible for priorities, who is responsible for facilitating the prioritization process and who is responsible for defining what processes are used to change priorities. If it is decided that business us responsible, utilize a single backlog that the business can see and let them fight over the prioritization with defined practices. Depending on the size of the company and overall development model I might use some framework (or pick suitable parts) like Less or SaFE to kickstart the new development process and then utilize larger scale retros to optimize the workflow continuously but in a structured manner.