This is based on a word game that as far as I know was invented by my friend's Dad.
The goal is to make as long a word as you can, starting from any three-letter word, using the following rule: You must always change one of the letters in the word, and you must always add a new letter to the word, and the result must always be a word.
So for example, you could start from
cat to get
cat fate [change the c to an f, add an e] grate [change the f to an r, add a g] graced [change the t to a c, add a d] cracked [change the g to a c, add a k] crackers [change the d to an r, add an s]
For 8 letters. Note that you can change any letter, and the letter you add can be at the beginning, the end or somewhere else. However, you have the following restrictions:
you always have to add one letter and change one letter
you can't add a letter and then change it in the same move
To be absolutely clear on that last rule: a move isn't allowed if it is possible to get from the longer word to the shorter one just by removing one letter. (Thanks to astralfenix for suggesting this clarification.)
Typical scrabble rules apply, e.g. no proper nouns.
In case of disputes regarding words of length 8 or less we'll use this word list, which I think is the one used for scrabble. For words longer than 8 characters, any reasonable dictionary will do. Whoever gets the longest word first will win. I don't know the longest possible word.