Project specific keys for all nested fields

Issue: I’m using CDA’s Select Operator with the include parameter set to 10. Somehow, the Select only removes the second-level deep.

Goal: I want to use projection (Select operator) for all those 10-level deep entries

eg.

"fields": {
              "title": "Services",
              "sections": {
                         "fields": {
                          "title": "Librarians",
                                        "fields": {
                                        "title": "Services > Librarians > Home",
                                                  ... so on

Figure 1

As you can see in Figure 1, metadata or sys object are not present for all levels and this is what I wanted. Is there any way to do this with just the CDA?

Note: We already agreed not to use the GraphQL API (it seems the only API that will give us this no-code selection tho)