There must be some clever way just to add to the literate list, but I don't know it. However, just today I had a very similar problem, for Matlab code. I simply went to the mcode.sty file, and copied the entire list of literate replacements, and then added mine. So the old one looked like this
\lstset{%
literate=%
{(end)}{\lstbasicfont (end)}{5} % black ``end'' when indexing last vector element
{({ }end)}{\lstbasicfont ({ }end)}{6}
{(end{ })}{\lstbasicfont (end{ })}{6}
{({ }end{ })}{\lstbasicfont ({ }end{ })}{7}
{:end}{\lstbasicfont :end}{4}
{:{ }end}{\lstbasicfont :{ }end}{5}
{end:}{\lstbasicfont end:}{4}
{end{ }:}{\lstbasicfont end{ }:}{5}
{,end}{\lstbasicfont ,end}{4}
{,{ }end}{\lstbasicfont ,{ }end}{5}
{µ}{$\mu$}1
{~}{{\fontfamily{ptm}\selectfont\texttildelow}}1 % get a nicer tilde character
}
and I changed that to
\lstset{%
literate=%
{(end)}{\lstbasicfont (end)}{5} % black ``end'' when indexing last vector element
{({ }end)}{\lstbasicfont ({ }end)}{6}
{(end{ })}{\lstbasicfont (end{ })}{6}
{({ }end{ })}{\lstbasicfont ({ }end{ })}{7}
{:end}{\lstbasicfont :end}{4}
{:{ }end}{\lstbasicfont :{ }end}{5}
{end:}{\lstbasicfont end:}{4}
{end{ }:}{\lstbasicfont end{ }:}{5}
{,end}{\lstbasicfont ,end}{4}
{,{ }end}{\lstbasicfont ,{ }end}{5}
{µ}{$\mu$}1
{~}{{\fontfamily{ptm}\selectfont\texttildelow}}1 % get a nicer tilde character
{×}{$\times$}1 % W.E.D. added on 1/18/2021
}
So, if you can find which package you are using that already defines a literate list, just copy and paste that into your document along with your addition.