Some shipper could set up containerized POD service, or piggyback, or even own the special boxcars, and hire a RR to handle them. Maybe they already do something like that. That's how various package companies use rail, and maybe (still?) some mail contractors. The problem, of course, is that household goods are generally off-line at both ends of the trip and even shifting the pods from one mode to another costs money and takes time.
What about handling private autos on routes where a given road always has to move empty auto-racks (if such routes exist)? That would be using existing cars in existing trains. Amtrak's auto-train covers all it's costs, I believe, so you'd maybe either a RR, or more likely a clever company with RR and auto distributor connections could put together a web-advertised service to move cars between major metropolitan areas -- the ones that are big enough that so many people move between them every day that you could usually fill one or two auto racks with the cars of the ones who'd rather fly, or only drive one of their cars, or whatever. Or maybe not; the service I'm imagining would only run in one direction on most routes and would require a fair amount of organizational support, payment to the auto companies to use their facilities and to someone to drive the cars onto the train, etc., and so might very likely not make business sense.