typically, the location will let you keep the same car. you cannot check it out over the phone or email, they need your signature on the contract.

Some managers with a wizard number have checked in cars and checked them out remotely, but this is the exception, not the rule. The rental agent can, with some knowhow, allow you to sign two contracts at pickup, "partial" the contract in the system, and backfill it to a specific date, but as I said before, you need a really good agent who knows how to do do this.