If you have a valid multi-day ticket you have the option to get "Fastpass Exchange Cards" for each member of your party but not for more than six people total. All members of your party must be present with you to get these cards.
The Cards are valid that day only at that Park only. When inserted in a Fastpass machine they will give a Fastpass for that particular attraction with the current time as the return time. Each Fastpass location will have at least one machine for these available, and it will be available even if the normal Fastpasses for the day have all been distributed.
That said, your choices and limits will vary by park, season, crowd sizes and other arcane factors, such as the phase of the Moon. Each park will have a flyer indicating the rules for that park for that day.