K, the 'Housesweep' with a 'midden name' is the female counterpart of S. They are often mentioned together but do not seem to interact much. 

Kate Strong, as is generally realized, was a tyrannical Dublin streetcleaner of the 1630s. Sir James Carroll, Lord Mayor in 1634, wrote of her: 'She is so much affected to profit as she will never find sufficient carriage to take away the dung, for where six carts are few enough to take away the dung of the city every week to keep it clean, she did and will maintain but two, which can scarce keep the way from the castle to the church clean, or that from the Mayor's house to the church, neglecting all the rest of the city, which she cleans but sparingly and very seldom... the more that she was followed the worse she grew, and kept the streets the fouler.'

Kate Strong was indeed a widow, but remarried with the merchant Thomas White thus permitting K and S in FW, theoretically at least, to be conjoined. Her two assistants, whose names suggest Shem and Shaun, were James Bellewe and John Butcher.

McHugh, Roland / The sigla of Finnegans wake

 
K 6) Where What means Summon in the Housewipe Housesweep Dina? Gellory be to the sails of cloth nowand I have to beeswax the bringing in all the muck of the parks to us and I thawght I knew the his stain on the flower and who broke the dandleass and who seen the rest of the plum goosebellies and who leff that there and who put this here & who put the jam pot in the yard and whatareyou whatin the love of the whatin the name of Sin Pollareyou rubbing the flowerofthe sideofthe flowerofthe parlourwith Shite will you have a plateful?

 

David Hayman - Joyce, James / A first-draft version of Finnegans wake (1963)