The Addams Family's latest addition, baby Pubert, has been abducted by his old nanny, Debbie Jellinsky.
She has left a ransom note stating, that if they ever want to see Pubert again, Gomez will have to sign over his half of the Addams Family's estate to her. At the end of the note she states that she will get in touch with Gomez in a few days to sort out the signing over of the deeds. Gomez and Fester, after a bit of detective work, discover where she is hiding with Pubert. They have tracked her down to an old mansion located just a few miles out of town.
The whole family set off in search of Pubert. When they arrive at the gates to the grounds of her mansion they decide to split up and go off in search of him. Miles and miles of gardens, swamps, mountains, rivers, deserts and caverns surround the mansion. Debbie has hidden herself away somewhere inside the mansion, inviting a few of her friends (fiends) to join her. Fester will have to use his skill, to avoid the traps, solve the puzzles and destroy the nasties.
Along the way the the other family members, who themselves have ventured into the grounds to rescue the baby, will help Fester. They will appear at different points in the game and offer advice or items depending upon what Fester has done so far. Fester will also find that not all of Debbie's fiends are loyal to her, some may be willing to help Fester on his quest, but usually only for a price.