Hi team, Is it possible to apply multiple filters in ReadRelationshipsRequest?

no it's not possible, you'd need to issue various independent ReadRelationship requests

I’m trying to get a list of entities a user can access and belong to an org

Please note read relationships does not compute effective permissions in the system, so you'd be making such inference by exploiting knowledge of the schema. That is subject to errors as the schema evolves. The API for this would be LookupSubjects. But it won't filter by org, so you'd have to do that at the application level.