In 1782, following the discovery of the obelisk buried under Campo Marzio. There were many ideas of where to place this obelisk, but the favorite idea tended to the placing it between the two horses in front of the Quirinale. Giovanni Antinori received the job, and he began dismantling the fountain of Monte Cavallo. Antinori made several attempts at pulling the colossal statues into their proper positions until he finally managed to successfully move them, and the task would not be completed until 1786. To make a joke of the situation the Romans created an anagram of the architects name, antinori became non tirai, meaning “I was not pulling”.
This new arrangement was met with both approval and criticism. The criticism can be seen through the following letter written by Milizia, "If you could see how the Horses at Monte Cavallo are arranged you would get angry, as anyone with eyes gets angry. But what really makes my blood boil is that these monuments were absolutely fine as they were. This idiot of an architect must be cross-eyed if he can't tell what's good from what's dreadful. Yet no one gives a hang and he's allowed to do whatever his crazy mind tells him." The statues also had something to say, they were vandalized with the inscription on one on the left-handed pedestal being changed from "OPUS PHIDIAE" to "OPUS perPHIDIAE Pii Sexti" (instead of "the work of Phidia," it became "the work of perfidious Pius VI).
Regarding the fountain, which was still in pieces, it was decided that “[the Spire] shall at once be perfectly cleaned, the said architect shall erect the fountain that, in accordance with his design, must be placed beneath the pedestal of the aforementioned Spire." Antinori decided to place the fountain to act as a drinking trough for animals.
The fountain would not be rebuilt until 1818, 32 years later, by architect Raffaele Stern, despite the proposals and declaration that Pius VI had carved into the pedestal of the obelisk, which stated that Pius ordered "the fountain with its jets of water to be rebuilt".
Pius’s new plan was to make use of the granite basin from the fountain in Campo Vaccino, atthe roman forum. Located behind the ruins of the Temple of the Dioscuri, it was built on the Aqua Felice conduit in 1593 by a stone mason named Bartolomeo Bassi. This was the order and design of Jacopo dealla Porta. Della Porta ordered for the fountain to be "a work of smooth white marble in accordance with the said drawing, with polished incisions to be well made by the able fellow."