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There are companies that offer this.
http://www.imoova.com/imoova/relocations https://www.transfercarus.com/
or you can try some of the larger RV rental companies directly.
Typically it's relatively short notice (up to a month or so), so you can't plan much in advance. It's unlikely that you can get a whole cross country trip at the dates you want. So it's a bit of a gamble, and during peak season, it may be difficult to find alternatives on short notice, if this one doesn't play out.