According to the ever racy Times Educational Supplement,
It is not beyond the realms of possibility for schools on very tight budgets to make really significant changes themselves
I love the idea of the realms of possibility. In my mind's eye I see a verdant and expansive kingdom ruled by a plump, benign queen. I don't know why Possibility should be female, but she is. And imagine what the border checkpoints are like! Imagine the customs officers! All those bootleggers trying to smuggle in four-sided triangles, Labour election victories and good D.H. Lawrence novels from the cloudy lands beyond.
Incidentally, realm derives from royal or real as in Real [Royal] Madrid, which was granted its royal title by the football-loving King Alfonso XIII.
A good poem by Sylvia Plath