Surely you'd just be employed by the internal HR company and on the books each product company would be contracting your services according to timesheets.
Real estate is a special situation with lots of subcontracting. They can make it work. In big multi-unit residential cities like NYC and Chicago, the doorman in that high-rise is in a union that provides all his benefits and has a set pay scale. The building ownership just contracts all that stuff out to the union. But that doorman can go work in some other building owned by some other owner too. You don't want that happening with your corporate employees developing and managing your consumer products.