Right element was「cave of yellow pornographic pus」(廣).「Both hand use and stink, loose and dripping in cavern」meaning to SPREAD something「wide」to WIDEN. Original glyph of「hand use」during「twenty or so, numerous」occurrences in a「wide space, cavern of flashes, cavern of flickering dull yellow light, pus, and porn」(擴). Numerous「flashes」in a wide and spacious「cavern」referring to sexual encounters. The witch-doctor shaman's service providers worked within speaking distance of each other, in those days moving from client to client, unknowingly carrying bacteria on their instruments and their unwashed hands.
　Up until a century ago or so in many hospital maternity wards around the world,「talented and skilled hands widened, spread illness」just as this glyph depicts: folks living in a city mostly were the ones using hospitals for births. Women in labor were lined in beds awaiting full dilation of the cervix prior to delivery of the infant, when a nurse「with skilled hands」would traverse the line inserting her finger(s) into the vagina of each woman in order to feel how large the cervix had dilated. After many hours of this and when fully dilated, a woman would be brought into the delivery area. Needless to say, if a single expectant mother among that day's group had a case of syphilis and/or gonorrhea (estimated quite conservatively to have been one woman in every seven, and a common occurrence today also: one in four teenage females have an STD), then every expectant mother down the line would be given a dose by the nurse's feeling fingers. Traversing the line in both directions over the course of a few hours made certain that everyone went home with more than just a new baby. Rural folks employed do-it-yerself [sic] techniques, or the pregnant woman's mother or other relative, or a midwife who worked one-on-one and was much less likely to spread an infection. More often than not the hapless husband was later blamed since a man who claimed to be loyal to his wife and to have nonetheless contracted gonorrhea or syphilis during marriage was generally not believed:「Training in obstetrics was rudimentary at best and was not compulsory for doctors until much later. In fact doctors were often the unwitting sources of infection for women in childbed, transmitting contagion from previous patients. Hospitals were places of last resort, sought only by the very poor and the desperate. The death rates in hospitals were known to be extremely high.」
　　[　https://adelaidia.sa.gov.au/subjects/19th-century-childbirth 2014-09-02　]　
　In the late 1840s:「…Dr. Ignaz Semmelweis was an assistant in the maternity wards of a Vienna hospital. There he observed that the mortality rate in a delivery room staffed by medical students was up to three times higher than in a second delivery room staffed by midwives. In fact, women were terrified of the room staffed by the medical students. Semmelweis observed that the students were coming straight from their lessons in the autopsy room to the delivery room. He postulated that the students might be carrying the infection from their dissections to birthing mothers. He ordered doctors and medical students to wash their hands with a chlorinated solution before examining women in labor. The mortality rate in his maternity wards eventually dropped to less than one percent. Despite the remarkable results, Semmelweis's colleagues greeted his findings with hostility. He eventually resigned his position. Later, he had similar dramatic results with handwashing in another maternity clinic, but to no avail. Ironically Semmelweis died in 1865 of Streptococcus pyogenes, with his views still largely ridiculed.」
　　[　link now-dead was http://www.accessexcellence.org/AE/AEC/CC/hand_background.php 2014-09-02　so instead see　https://www.academia.edu/43159762/Handwashing_　2023-05-17　]　
　「The rise of maternity wards in hospitals meant that many women gave birth within shouting distance of each other. Doctors, in those days before germ theory, went from patient to patient, unknowingly carrying the bacteria on their instruments and their unwashed hands.」
　　[　https://www.mentalfloss.com/article/50513/historical-horror-childbirth 2023-05-18　]　 how much more so among the prostitutes?

Modern definitions (that generally disregard history) …excluding politically incorrect concepts and other meanings deemed offensive today; may list only pigeonholed definitions, euphemisms, or meaningless mnemonics)
Chinese: Japanese variant of 擴|扩
Japanese: spread, span, expanse, extent, to spread, to extend, to stretch, to reach to, to get around, to fill, to expand, to enlarge, to widen, to broaden, to unfold, to open, to unroll, to unwrap, to scatter about, to spread around, to make flourish, to cause to prosper
Unihan extended: expand, enlarge, stretch
EDRDG: broaden; extend; expand; enlarge