How to implement such a "second-level" personal screen?
Solution to share:
Ask a ABAP programmers to create a completely empty ABAP transaction. That isn't a lot of work! Then assign multiple custom transaction codes to that one ABAP program, one tcode for each second level screen you require. Use those transactions to create your second-level menus.
One can create a ABAP program which contains multiple transactions. In Personas one can use all these transactions. For each of the transactions, one can modify the copy of the ABAP program UI, and these UI can serve as the second-level menu UIs.