Indeed I recognize some of these names. Captain John Dachsteder married Sarah, Catherine's mother, who appears to have been the neice of an Onondaga chief whose English name has not yet been determined (the Journal of John Norton gives his name as 'Kaneahintwahte'). In a newspaper article of September 2, 1801, "Wentworth Bygones", it is stated that,
"... Dr. Tiffany visited John Dockstader's wife Mrs. Dockstader, alias Mrs. Burns, alias Sally Ann Van Gorder."
What exactly the two additional surnames signify is not known, but the latter may represent Sarah's full unmarried name.
As of now it appears that Chauncey Burnham initially married Catherine's older sister Warri (Mary), who seems to have died before about 1803. Chauncey then married Catherine, and after a few children Chauncey also died. The widowed Catherine then married Chauncey's brother, Lyman Burnham, and they had more children. This whole Widow-marries-sibling-of-deceased-spouse routine was not uncommon in those days and has happened in other branches of my own family. According to some sources, Chauncey appears to have also eventually died and then Catherine married yet another Burnham brother, Oliver.
Discussion of John Dachsteder's ancestral holdings by a surveyor for the City of Brantford in 1835 cites "Catherine and John Burnham" as the rightful heirs to those lands which hadn't been usurped by Benjamin Canby and converted into Canborough. Who this "John" is I'm not entirely sure, but Catherine's oldest son by Chauncey would appear to have been "John Burnham", so he may have married another woman named Catherine and inherited John Dachsteder's land by 1835.
Erlene Dudley and Debbie St. Louis (descendants of John Dachsteder through two other children of Catherine) have done quite a bit of research on the family so you might also want to contact them. Erlene can be emailed at William Woods University (director of Dulany Library) and Debbie St. Louis has posted some messages below.