I love a mystery! If you do, too, arm yourself with the proper tools -

Get the 1901 Census Extractor from the Leeds Indexers page. Make sure you get version 4.0.2. (They also have a replacement file for earlier versions, but if that's too complicated, just download the new version if yours has stopped working correctly.)

http://leedsindexers.co.uk/Main-Internet%20Tools.htm

Search for Clara's and capture the data. Search for Florence's and Florrie's, etc. and capture the data. Check the parishes any matches are in and grab all the female Corletts in the parish. Sort the data and look for matching Person ID's...

Unfortunately, I was unable to find any household containing all three females... But it was fun trying. Maybe I just didn't look hard enough and you, being an ispired family member will do better. Good luck!

BB