Query with AND operator across inner hits of a document?

[cphramington (Chris)]

I'm currently using a query like this to prioritize hits that contain multiple terms from the query string over those that contain fewer.

                     "nested": {
                          "path": "my_nested_field",
                          "query": {
                                "bool": {
                                    "should": [
                                        {
                                            "query_string": {
                                                "query": query_str,
                                                "default_operator": "AND"
                                            },
                                        },
                                        {
                                            "query_string": {
                                                "query": query_str,
                                                "boost": 0.5
                           }}]}}}

I'd like the scoring to reflect:

1. Hits that contain the all of the query string terms in the same "my_nested_field"
2. Hits that contain the all of the query string terms across all nested "my_nested_field"s in the same document
3. Hits that contain fewer than all of the query string terms

I know that BM25 doesn't take into account number of individual terms matched in the document, which makes this a tough problem, but are there any sort of other heuristics to maximize scores for documents whose inner hits contain the highest number of found search terms?