I would look further into why she is overgrooming. My Milly had also been overgrooming, she had a blood test which showed elevated levels of eosinophils which at first we thought were due to a flea allergy, but she carried on when there were definitely no fleas. Then (several months later) it dawned on me...I had swapped her from the RC outdoor mature onto the RC Ageing 12+ when they changed their range. I checked the ingredients and bingo - the 12+ has high levels of wheat, which the previous one didn't. I have swapped her onto a grain free food and she has stopped overgrooming and her beautiful fur is now growing back.
Generally speaking, I don't think cats overgroom 'for fun' so it's a case of trying to unpick what the cause might be. If she is clean and flea free, then I would suspect either stress or some kind of food intolerance as two high possibilities.
Good luck!