I am not sure whether you know the functionality and difference between Customer Consignment and Vendor Consignment.
As per the first para, the process is related to Third Party scenario and your next paras explains about customer consignment. You can have both these process with separate document types and configuration. That is whenever, your client would like to delivery from vendor stock, raise a PO on vendor and follow the third party sales process.
On the other hand, whenever your client would like to deliver from own stock, have a warehouse to which, the stocks can be transferred which would be treated as a special stock with movement type 631W. As and when customer requires, you can create a consignment issue order and deliver the material.
G. Lakshmipathi