There are two girls named "Epes" in the rolls of the Mordecai school. Catharine/Catherine Epes was at the school for two years, 1813 and 1814; Elizabeth was there for all of 1817. There's a Thomas Epes associated with Catharine's account, and a William B. Cowan might have been acting as guardian for Elizabeth. They're from Virginia, from my notes.
Note that the common Virginia surname Epes can also appear as Epps or Eppes. We've already met one Mordecai girl with the name Eppes as her middle name, Sarah Eppes Doswell Cabell -- so she's a possible school connection to Catherine and Elizabeth Epes too.
So this was maybe easier than I expected: Catherine Williams Epes Green (1802-1887), daughter of Thomas Epes and Catherine Williams, married William B. Green in 1827. Catherine's uncle John Epes had daughters Catherine Grace Epes Cowan (who married William Bowie Cowan) and Elizabeth Campbell Epes Jones (1803-1880), who married Richard Jones in 1818. So Mordecai students Catherine and Elizabeth were first cousins. Fellow student Sarah Eppes Doswell was another cousin; Sarah and Catherine had their Williams grandparents in common. Elizabeth's mother was John Epes' second wife, so she wasn't truly first cousins to Sarah Doswell, but these families were all very much entangled. Congressman Sydney Parham Epes (1865-1900) was one of the Epes' girls' distant nephews, and Congressman James F. Epes (1842-1910) seems to be from the same extended family.
How does William B. Cowan come into the story? Elizabeth Epes's father John died in 1816, so it makes sense that her older half-sister's husband, Cowan, paid Elizabeth's accounts at the Mordecai school the following year.
Catherine Epes Green doesn't seem to have had any children in her long life; Elizabeth Epes Jones had about eight children, maybe more. Both women lived through the Civil War and into old age, and as far as I can tell neither ever lived away from Virginia--except for during their schooldays in North Carolina.