The supplier documented quality system must describe Good Engineering practices and Good Documentation practices. In addition to the quality system a Project and Quality Plan must be written for project specific items. This will reduce a lot of noise in the communication during the project. All project members must be aware of that plan and must live according the plan.
The project will run smooth with supplier with a formal quality culture and has the core business in the Life Science industry. That care must be given to suppliers that work occasionally in the Life Science industry.