LaTeX is very good in adjusting the numbering -- and more importantly the references to it -- when inserting new chapters, sections, etc.
Legal documents (and books), at least here in Germany, tend to insert these things by keeping the previous numbering intact, but using the number before the insertion followed by a small letter (a, b, c, ...), to indicate that something has changed (either at the last minute, or -- which is the really important case -- from a previous edition).
Since I thought it rare that there would be more than one additional consecutive footnote, I tried the following (incredibly crude and dirty) hack, shown in the MWE:
\documentclass{article}
\newcommand{\myextrafootnote}[1]{\renewcommand{\thefootnote}{\arabic{footnote}a}\footnote[\thefootnote]{#1}\renewcommand{\thefootnote}{\arabic{footnote}}}%
\begin{document}
This is the old text\footnote{foo}, followed by the new insert\myextrafootnote{New Exciting Stuff!!}, followed by the old next one.\footnote{bar}
\end{document}
Sadly, it doesn't work as I had hoped. While the footnotes themselves look as they should:

the text gets the additional a also added just before the footnotemark: as shown here:

Ideally, of course, the a would also come from some form of counter (I tried that too, but it turned into lots of error messages about missing arguments, so I abandoned it and decided to better ask the experts...) so if there were more than one additional consecutive added footnote, it would still work correctly [and be less crude than it is now].

\newcounter{extrastuff}[footnote]. – GuM Jun 09 '16 at 12:43\newcounter{extrastuff}[footnote]would be easy, of course – Jun 09 '16 at 12:51\alphwith\Alph. Instead of displaying the whole footnote marker superscript, just the number is superscript and the following letter is printed normal size on the line. Any idea why? – richard Jan 07 '17 at 12:54\Alphtoo. I don't know what you have done instead. – Jan 07 '17 at 16:56