Hi,
Document types are designed /created based on different procurement processes in an organization not based on company code.
In your case, you can create purchasing groups PGA for User A for company A, PGB for User B Company B and PGC for User C for company C.
Consult Basis Consultant and based on purchasing groups you can restrict creation of purchase order with purchase order document type by authorization with authorization object as following:
1. 1. Creation of purchase order for document type 1-3 for purchasing groups PGA with company A with help of authorization.
2. 2. Creation of purchase order for document type 4-6 for purchasing groups PGB with company B with help of authorization.
3. 3. Creation of purchase order for document type 7-9 for purchasing groups PGC with company C with help of authorization.
Regards,
Biju K