a change in government means different goals and fears so its very important just look at the change between LBJ and Nixon. Pitt's ambition was to take all of France colonial empire, I personally don't think that would be wise but defiantly possible if the dominoes fall right, although I struggle to think how they could hold on to it even with heavy handed tactics in the Caribbean because of the economic, and military realities of conquering that land especially Haiti, because they almost did in OTL look at France's colonial empire before and after the Seven Years War. I do think if Pitt stayed in power it would have affect the peace deal if the events off the Seven Years War stayed the same and doubly so if Great Britain didn't loose Menorca which is possible if orders hadn't gotten confused. Also would the diplomatic consequences be that much then OTL because Great Britain was hated by Europe even with the softer peace deal.
Ok let’s set some timelines and parameters. The 7 year war lasted 1756-1762/63.
During that time Pitt was never prime minister, he was the “foreign minister” or as know minister of southern department. During the 7 year war there were about 4 prime ministers but Pitt only became prime minister in 1766 to 1768.
While there were those who wished to rob France of all its colonies the government and other politicians and powerful Englishmen did not want to turn all of Europe against Britain.
If we are to follow through on your comment aboutEnglsnd keeping all it had captured then it would of also kicked France out of India and Africa. But it would of lost the opportunity to convince it to swap territory with Spain during the negotiations and France would still been a danger to the 13 colonies in north America.
Instead it used its strong position to strike several territory swapping arrangements
The French gave up parts of its North America to Spain. In return it received Carribean, Grand Banks, Africa and India. Although it’s indus territory lost much influence.
So what was important for England/Britain in the negotiations.
1) stop siege of Gibraltar
2) secure 13 colonies from attack by French is hostile native tribe allied with France or other foreign power.
4) control all of North American continent north of Florida
5) gain Menorca back
6) gain the upper hand in India
7) END WAR
All of these it did by giving some territory back to France and establishing while at same time establishing Britain as most powerful country.
So what would of been accomplished by a more aggressive stand, continuation of war, loss of leverage in negotiations and antagonising European powers even more than they did.