There are 24 hour cards and 72 hour SL passes that are not plastic cards. They are paper cards with a small chip inside and they get activated automatically at first use. This doesn't require buying a plastic card at 20SEK or any other price, but it does involve buying these SL 24/72 hour passes from a staffed sales outlet. Tourist information offices seem to sell them.
It is one card per adult. Young children are free, but this may mean you have to go via a staff-controlled gate area to get in or otherwise be quick to clear the child and adult together at the automated gates.