The refit is named the "Columbia Class" and both the NX-01 Enterprise and NX-06 Endeavour have been refitted to it during or after the Romulan war.
What is the extra addition body section supposed to do for the ship anyway? I can see an advantage to having more internal space. But given that the ship retains the original twin warp engines wouldn't speed, range and malnuverablity be seriously reduced?
In the novels, the secondary hull is nested within the second half of the warp field so it doesn't affect warp flight.
It now holds shuttlebays in the sides, the new warp 6 engine and engineering (the old engineering section is reused for more mechanical changes to the saucer) and a new deflector assembly. The old one is reduced to a secondary spare.