The JR train companies sell a ticket package at various times of the year, usually during holiday and other popular travel times, called seishin jyuhachi kippu. This ticket is actually 5 tickets, each good for 24 hours of travel on the JR system trains. More than one person can travel on the ticket on the same day, as long as there are enough unused ‘days’ on your ticket.
If you don’t want to, or can’t, use all 5 tickets, try a ken-ken shop: they’ll often sell unused portions, or even buy your unused portions. It’s best to contact the shop ahead of time and arrange the special deal.