Extend the "General" tab in the "My Setting & Tools" page Follow

I have some per-user settings that I want my plugin to expose to users through some sort of form they can edit.

Is it possible to add a compact form in to the 'General' tab in the My Setting & Tools page (i.e. /profile.html).

I've circled it in orange in this picture:

I would also settle on just having another tab next to 'Notification Rules' if that option is better/easier.