Radical empathy was a more proactive approach to empathy which involved considering and being open-minded about a point of view or perspective, even if it were different and disagreeable from one's own.
In 2259, the United Federation of Planets sought an alliance with the R'ongovian Protectorate. Captain Christopher Pike realized that the R'ongovian diplomats were rude to the Tellarites, reasonable with Humans, and deeply logical when talking to a Vulcan. Pike initially thought that R'ongovians copied anyone they came into contact with, but it occurred to him that it might have been a diplomatic technique. Pike postulated that the R'ongovians were looking for somebody to take their point of view and that what they valued the most in others was the capacity to see things their way.
The R'ongovians feared the loss of their culture through homogenization with a multilateral alliance such as the Federation. Pike employed radical empathy by saying that they shouldn't ally with the Federation for a number of reasons. The alliance would turn Federation enemies into R'ongovian enemies, the Klingon War was still recent, the Romulans were biding their time, and other species could become angry with them next. The Federation also didn't approach the R'ongovians with any great respect for their culture as they barely knew anything about it. Pike admitted that it was clear the Federation was only interested in the R'ongovians for their territory. In return for an alliance, the R'ongovians would get the hypothetical benefit of new trade markets, scientific advancement, and promise of support in the event of a crisis which would probably only exist because of the alliance in the first place. Pike finished his statements by saying that the Federation had lots to offer, but it always exacted a price, a price which the R'ongovians had good reason to suspect was too high for them to pay. The R'ongovians, who believed empathy to be a hallmark of their people, accepted the alliance and flew the flag of the Federation from their solar sailship. (SNW: "Spock Amok")