Thank you for your query.
You may use the API - 'SEQ-case-save-and-screen-cases: Save and screen multiple cases' call to screen multiple entities using a single API call.
You can feed up to 50 entities in a single API call.
Please note: This is asynchronous API call and you will have to use API call - 'SEQ-case-screening-statuses: Retrieve screening status for multiple cases' (also supports 50 cases per call) in order to check if the case has been screened or not before fetching the case results.
Hope this answers your query.