Possibly the following file contains more options, though admittedly I have not spent much time looking for them. This is the file that contains the information used by SyntaxInformation

ToFileName[{$InstallationDirectory, "SystemFiles", "Kernel", 
  "TextResources", $Language}, "FunctionInformation.m"]

This file contains a lot of options, both "Symbol options" and "string options". Not all "kinds of options" are listed here, at least the "option" "OptionNames" of SyntaxInformation is not present here. The file also does not appear to contain nested options.