S corp cannot:
A. Have more than 100 shareholders.
B. Have as a shareholder a person who is not an individual (except an estate or certain trusts).
C. Have a nonresident alien as a shareholder.
D. Have more than one class of stock.
The acquisition of shares of another S corporation by an S corporation will result in the prohibition under (b) above. Therefore, the answer to your question is no, an S corporation cannot own shares of another S corporation without voiding the acquired S corporation's Sub-S election.
An exception exists that allows an S corporation to own 100 percent of another S corporation. In this case, the subsidiary is ignored as a separate entity for income tax purposes and all its income and expenses are included as part of the parent company's tax return without distinction. So the real answer to your question is none or all.