Magento 2 REST API – default to `all`?

We have a 3rd party integration using the /rest/V1/product/[sku] Magento endpoint, but some updates have not been coming through to the admin (single store) – we tracked down that changing the endpoint to /rest/all/V1/product/[sku] fixes the issue (admin reflects updated status), but we do not have access to change the endpoint with the 3rd party.

Is there a way to modify the product scope within the endpoint? ie, something like:

if ($product->getScope() == Scope::DEFAULT) {
    $product->setScope(Scope::GLOBAL);
}

before the product gets updated?