SHORT ANSWER: NO
The 3 buttons are really designed to work as a ‘CALL TO ACTION’, so any more than 3 on the home page, is a bit overkill. And, I ran out of room, so I couldn’t really fit any more than 3.
So if you really want more than 3 buttons, it can probably be done, but it’s not going to be easy. I would focus on using the 3 Call to Action buttons to link to the MOST important pages in your site, then place additional links in the ‘info boxes’, which can also act as a call to action type of link.