Question:
The Owner of a Document Change Control wants to add a new Owner to the Sharing Settings in Vault. However, the Owner can not be selected and added through Add Manual Assignment. Why is this?
Answer:
The state of the Document Change Control is in Approval. There is a task that is assigned to Approver(QA Approver) to approve. When the task is completed, the new Owner can be added to the Sharing Settings.

A Vault Owner can add a new Owner at any time, regardless of whether or not there is a task assigned to Approver(QA Approver) to approve.
Related Documentation:
Vault Help Documentation: Configuring Multi-Document Change Control