Do any tours include climbing the Dome in the Basilica of St. Peter’s/Florence Duomo/etc?

No, none of our group tours include in price or Itinerary a climb to the top of St. Peter’s/Florence’s Duomo/etc. The reason being that it is a physically demanding activity and takes quite a bit of time as well, which would exclude or disinterest many of our guests. But your Presto guide will be happy to indicate where you can go to do so after your tour is completed, should this be something that interests you! As for Private tours, they do offer flexibility in itinerary, so climbing the Dome with your Private Presto guide is definitely an option.