Yes you can! Global Attributes provide a way to reference an Attribute at the Organization Level for your EDI Projects. Global Attributes allow an Attribute's generated value to be referenced by multiple Projects without the need to perform the same steps to configure the Attribute in each Project.
You can set up a collection of Global Attributes with their own Generator configurations and then reference them via Test Data Cases as needed. For more information, please see this article: Global Attributes Overview.