Three thousand years of layers, and the best carbonara within a mile of anywhere.
This is a shape, not a schedule. Each day has two anchors and a lot of slack, because 3-day itineraries that book four things a day fall apart the first time lunch runs long. Move things around freely — the neighbourhoods are grouped so that walking between stops actually works.
Rome's constraint is restaurant capacity — trattorias are small and won't seat six without notice. Assign one person to book dinners before you fly and keep the reservations somewhere everyone can check.