Are they on a single ticket? If so, they are rather flexible regardless of the fare class.

If not, they may try to charge you for a new ticket if it's a Red E-deal one (some fare buckets are apparently completely non-changeable on the day).

No problem changing it on the day if it's a Flex fare. I have never been paid a cent extra to change it on the day when transferring from an international flight on a separate ticket as long as I am on a Flex domestic fare.