Multiple nested sorts dont work

we have a situation where treatment has a price and hospital may or may not want to display it.
so there is a price field PLUS a lp_low_priority field.
value of lp_low_priority is 1 (true) when price is not set(price is_null).

Vendor doc is saved with its nested products.
when user searches for treatment he get list of hospitals with minimum price of the treatment.
now the sort works fine.
BUT i want the hospital with that treatment with the lp_low_priority = 1 to come at last.

    {
      "properties":{
        .....
          
          "treatments":{
              "properties":{
                  "child_of":{
                      "type":"integer"
                  },
                  "hospital_id":{
                      "type":"integer"
                  },
                  "id":{
                      "type":"integer"
                  },
                  "keywords":{
                      "type":"string"
                  },
              "procedure_count": {
                "type": "long"
              },
                  "status":{
                      "type":"string",
                 "index":"not_analyzed"
                  },
                  "treatment_id":{
                      "type":"integer"
                  },
                  "treatment_name":{
                      "type":"string"
                  },
                  "treatment_price":{
                      "type":"integer"
                  },
                  "treatment_slug":{
                      "type":"string",
                      "index":"not_analyzed"
                  },
                  "treatment_status":{
                      "type":"string",
                 "index":"not_analyzed"
                  },
              "low_priority": {
                "type": "integer"
              },
              "lowest_price": {
                "type": "integer"
              },
              "highest_price": {
                "type": "integer"
              },
              "lp_low_priority": {  
                "type": "integer"
              },
              "hp_low_priority": {  
                "type": "integer"
              }
              }
          }
      }
  }

the code to search it is like

 {
          "sort": [
            {
              "treatments.lowest_price": {
                "nested_filter": {
                  "term": {
                    "treatments.treatment_slug": "heart-surgery"
                  }
                },
                "mode": "avg",
                "order": "asc"
              }
            },
            {
              "treatments.lp_low_priority": {
                "order": "asc",
                "nested_filter": {
                  "term": {
                    "treatments.treatment_slug": "heart-surgery"
                  }
                },
                "mode": "max"
              }
            }
          ],
          "query": {
            "filtered": {
              "filter": [
                {
                  "term": {
                    "treatments.treatment_slug": "heart-surgery"
                  }
                },
                {
                  "term": {
                    "treatments.status": "active"
                  }
                },
                {
                  "term": {
                    "treatments.treatment_status": "active"
                  }
                },
                {
                  "term": {
                    "hospital_status": "active"
                  }
                },
                {
                  "terms": {
                    "location.country": [
                      "India"
                    ]
                  }
                }
              ]
            }
          }
        }

the result is way too weird.
if I only use

 {
              "sort": [
                {
                  "treatments.lowest_price": {
                    "nested_filter": {
                      "term": {
                        "treatments.treatment_slug": "heart-surgery"
                      }
                    },
                    "mode": "avg",
                    "order": "asc"
                  }
                }

The sorting is in order but then you see the `lp_low_priority` come first in order, which is OK(but not the requirement).

can i use multiple sorts?