Unable to update item of a specific organization via REST PATCH request.

We have items which are currently master controlled and are made available across multiple organizations(Both master and other child orgs). The itemId is same across all the organizations. When making an update to an item via REST PATCH api, how do we specify the orgId under which this update should apply? Is there a mechanism or configuration to make controlled updates at organization level? I would ONLY want item to be updated under specific organizationId.