How about this: I'll start with a word. The next person can either:
1. Rearrage the letters, or
2. Change exactly one of the letters, or
3. Both (rearrange AND change exactly one letter).
So, for example, if the word were SLINK, you could change it to:
KILNS (rearranges the letters of SLINK)
SLUNK (changes exactly one letter of SLINK)
LINES (changes the K in SLINK to an E and rearranges the letters).
And the word is:
HEART