The term 'greatest possible' can be broken down into four crossword solutions: MAXIMAL (7 letters), ALL (3 letters), NTH (3 letters), and ULTIMATE (8 letters). MAXIMAL means the highest or greatest degree or amount possible, while ALL means the whole quantity or extent of a particular group or thing. NTH is an ordinal number that indicates the position in a series, such as first, second, third, etc. Lastly, ULTIMATE means the best or most extreme example of its kind. Together, these four words indicate the highest or most extreme degree or amount of something that is possible.