Puzzle of the Week # 535 - Three Sets of Words

These words have been grouped into three sets of three words according to some property.

The fact that there are three sets is a big clue. What is that property and why would trying the same thing with only two sets of words be practically impossible?

 

PYJAMAS

MAYDAY

SAVVY

 

BETWEEN

WHEEZE

TENTH

 

COLOURFUL

CRUCIFIX

FLOOR