Currently, for groups your organize, you can customize colors and text, along with the options to show or hide the team roster, media gallery, team schedule, documents, sponsors, and linked groups.
Could you tell me more about what else you would like to configure? Is the ability to move modules around satisfactory? Are you interested in having more control, such as the ability to edit your own html layout?
Unfortunately, we don't currently provide away to add anything but text to that whitespace area. I definitely agree that we should figure out a better way to day with that space--perhaps a rework of the team public page layout is overdue.