Someone correct me if I'm wrong, but if any of the "next-day" checks (other than on us checks) are not deposited into an account of the payee, then they are no longer next day and are subject to the 2/5 day availability depending on whether they are local or non-local (except Treasury and U.S. Postal money orders which would be given 2 days regardless of whether they are local or non-local).
As far as I know that is the only exception for third-party checks.
You can find this in 229.10 and 229.12.