Can we add test cases to a Test run by the "test case ID" via API

The API takes an array, so just pass in multiple objects, e.g.:

curl -L -X POST 'https://app.testiny.io/api/v1/testrun/mapping/bulk/testcase:testrun?op=add_or_update' \
  -H 'Content-Type: application/json' \
  -H 'X-Api-Key: <API_KEY_VALUE>' \
  --data-raw '[{
      "ids": { "testcase_id": 1234, "testrun_id": 3 },
      "mapped": { "result_status": "PASSED" }
    }, {
      "ids": { "testcase_id": 12345, "testrun_id": 2 },
      "mapped": { "result_status": "FAILED" }
    }]'

You can specify any test case and any test run, so you could also update multiple test runs in one go.

Regards,
Alex