Der er virkelig ingen god løsning, undtagen at sammenkæde AND'er:
SELECT * FROM myTable
WHERE title REGEXP "dog"
AND title REGEXP "cat"
AND title REGEXP "mouse"
Det regulære udtryk ville ellers se sådan ud:
SELECT * FROM myTable
WHERE title REGEXP "(dog.*cat.*mouse)|(dog.*mouse.*cat)|(mouse.*dog.*cat)|(mouse.*cat.*dog)|(cat.*dog.*mouse)|(cat.*mouse.*dog)"