As has been discussed in this meta post, there is a third party search (with $\LaTeX{}$ support) engine for Mathematics Stack Exchange. I was wondering whether there is search engine with similar functionalities for both MathOverflow and Meta-MathOverflow.

My questions are,

Are there any such search engines?

If not, then can anything be done regarding "installing" such a feature to this website?

`site:mathoverflow.net`

at the end of a Google search already gives a third-party search engine. If the important point here is the Latex support, you should probably mention it in the question. $\endgroup$