The term 'Third Way, Maybe' is a political philosophy that was popularized by former British Prime Minister Tony Blair. It is based on the idea of finding a middle ground between traditional left-wing and right-wing ideologies. The crossword solution for this term is 'RECOURSE, ' which means to turn to a higher authority or to seek help from someone else. This is in line with the Third Way, Maybe philosophy, as it suggests that people should look to outside sources for solutions to their problems.