Short answer is none, but that's a really tricky question for a few reasons. Many "loyalists" just simply weren't patriots. They didn't impede American liberty but saw little benefit to a war in the name of it. These would be more appropriately called neutralists than loyalists but non-historians tend to see an A. or B. without much exception or grey area between loyalist and patriot. In reality, it is likely that the majority of American colonists fit into this third category.

Actual loyalists actively opposed seperation and took steps to speak (and/or act) against it. One that immediately comes to mind is Joseph Galloway. Elected to Congress in 1774, there he proposed the Plan of Union in which America would remain subjects to the crown but gain some autonomy (this was very similar to Benjamin Franklin's 1754 Albany Plan, written by Franklin when he was still very loyal to the crown himself). The plan was refused and the Articles of Association signed instead, creating an American Nation for the first time (Franklin was a patrot by the time of his return from England and presentation of the Plan of Union, and the next year Franklin would submit a new government charter independent from England, which was also refused by Congress). Galloway would not serve in another congress and after the war started he joined the British ranks. He and his family were essentially exiled (by force) and they subsequently fled to England. This was a typical story of prominent loyalists repeated throughout the colonies/states. Franklin's own son, William (who was the royal Governor of New Jersey), would be exiled as well. Isaac Low is another congressional loyalist that likewise served in 1774. He fled New York with the British when they withdrew, surrendering the city back to the Americans.

As far as representation of goals, the big one was just to remain united. Once seperated many loyalists fled for other colonies or to England itself (believed to be about 60,000 in total with 10,000 alone settling in Canada). Some politically active loyalists remained so, most specifically in trying to establish amity between the nations and primarily regarding trade (such as Galloway did while in England), but most just went on with their life. But these weren't Americans; they were still subjects of the crown.

As for those who stayed, they typically quitely integrated back into society without much clamor of political views (having faced severe backlash and violence for being loyalists). I recently wrote another [answer] (https://www.reddit.com/r/AskHistorians/comments/gtgfll/what_happened_to_prominent_americans_who_sided/) about loyalist treatment and how the Treaty of Paris called for conciliation between the factions that you may find interesting as well.