Why? Is this generally regarded as utterly impossible or what?
The main change is that Britain has to give the colonies a decent compromise between representation and autonomy in some way. If they succeed, the colonies could stay "British" or rather could stay within a common entity with Britain indefinitely.
Britain offered fairly generous terms to the rebels twice during the 1770s, the second time in 1776 requiring little more than nominal acceptance of British soverignty and continued access for British merchants to American trade which fell within the limits of what some rebel leaders had said on the previous occasion would be considered acceptable, but those terms were rejected by hardline rebel leaders -- who had apparently already decided to settle for nothing short of full independence, without necessarily consulting their colonies' legislatures on the subject -- on both occasions. According to the book in which I read about this fact
(title = 'Redcoat', author's name I can't remember, written to accompany a television series) one reason for the refusal was that one of the main channels for British communication with the rebel leadership was through Benjamin Franklin who was serving as the rebels' ambassador to France, and
(according to claims that the author said had subsequently been made by John Adams) Franklin was taking an [unofficial] commission out of the French financial aid to the rebels which actually gave him a personal motive for prolonging the conflict...
And if too many of the rebels keep refusing terms then, unfortunately, Britain simply can't afford the troops necessary to maintain control effecively over such a large area.