KaTeX already supports math-mode accents, but doesn't support any of the usual accent commands in text mode. According to this list of text-mode LaTeX accent commands, we're missing:

• \`{o}
• \'{o}
• \^{o}
• \"{o}
• \H{o}
• \~{o}
• \c{c} (cedilla): ş
• \cb (comma below): ȘșȚț
• \k{a} (ogonek): ą
• \l{} (barred l): ł
• \={o}
• \b{o} (bar-under accent): ο̩
• \.{o}
• \d{u} (dot-under accent): ạ
• \r{a}
• \u{o}
• \v{s}
• \t{oo}: (tie-after accent): a͡
• \o

A lot of these should be straightforward by translating into Unicode, using combining characters.