I recently accepted a job offer. My start date is next week. I was interviewing with another company, which just invited me back to the second interview. I am more interested in the other company. How can I gracefully back out of the offer already accepted?

Gracefully? Probably not. They acted in good faith and offered you a job you were willing to accept. Your reneging puts them in a difficult position. Once you accepted, they began contacting candidates they rejected when you accepted. Now, they must contact those people again and reopen the search.

Can you back out? Yes, you can, but there are consequences, so be willing to accept them if you rescind your acceptance. You will be burning a bridge. Your reputation with the company that you are leaving in the lurch will suffer. You most certainly will not be able to go back there to seek employment again. Five or ten years in the future, you may be applying for a job somewhere else and discover that the person who hired you is now the hiring person at that company. Finally, you are risking a guaranteed job for one you might not get, and you may end up with no job.