Elasticsearch Conditional based querying

I'm working with Elasticsearch and have documents with fields that can be empty (""). Here's an example of the document structure:

    [
          {
            "company_code": "ABC",
            "client_id": "12345",
            "section": "abc",
            "module": "substitute",
            "priority": "1"
          },
          {
            "company_code": "ABC",
            "client_id": "",
            "section": "abc",
            "module": "buy_it_again_products",
            "priority": 1
          }
          {
            "company_code": "",
            "client_id": "",
            "section": "abc",
            "module": "buy_it_again_products",
            "priority": 1
          }
    ]

I need to create an Elasticsearch query that follows these conditions:

1. When company_code, client_id, and section are given, return documents matching all three fields with non-empty values.
2. If no documents match the first condition, then only return documents where company_code and section match, but client_id is empty ("").
3. If no documents match the first and second conditions, then only return documents where only section matches, and both company_code and client_id are empty ("").

The response should include documents satisfying only one condition according to the priority listed above. I have tried the following query and also msearch.

{
  "query": {
    "bool": {
      "should": [
        {
          "bool": {
            "must": [
              { "term": { "company_code": "ABC" } },
              { "term": { "client_id": "12345" } },
              { "term": { "section": "abc" } }
            ],
            "boost": 100
          }
        },
        {
          "bool": {
            "must": [
              { "term": { "company_code": "ABC" } },
              { "term": { "section": "abc" } },
              { "term": { "client_id": "" } }
            ],
            "boost": 20
          }
        },
        {
          "bool": {
            "must": [
              { "term": { "section": "abc" } },
              { "term": { "company_code": "" } },
              { "term": { "client_id": "" } }
            ],
            "boost": 1
          }
        }
      ],
      "minimum_should_match": 1
    }
  },
  "sort": [
    { "_score": "desc" }
  ]
}

The issue with this approach is, this returns all the documents matching all three conditions. Any way can get the expected result through ES?

The current version of Elasticsearch (8.17) does not offer a solution for this complication. A workaround is to perform a msearch and handle it on the server side.