Here I implemented an environment addendum, in which equations and optionally sections or subsection are numbered the way you want. It has an optional argument, which may be section or subsection and a mandatory one for some text to describe the inserted part.
So if you want to add a section, write
\begin{addendum}[section]{...} \section{...} text and equations here \end{addendum}
For a subsection write
\begin{addendum}[subsection]{...} \subsection{...} text and equations here \end{addendum}
And if you only want some text and equations
\begin{addendum}{...} text and equations here \end{addendum}
Note that addendum environments cannot be nested in one another. This is because LaTeX counters, which are used for saving the originals, are always global.
In the example, the Addendum line, the rules and the blue color are just there to better see the added parts. You can change that to your needs (see comments in code).

The code:
\documentclass{book} \usepackage{xcolor} \makeatletter % counters to store the original ones \newcounter{orig@section} \newcounter{orig@subsection} \newcounter{orig@equation} \newenvironment{addendum}[2][]{% \begingroup % save current counters \setcounter{orig@section}{\value{section}}% \setcounter{orig@subsection}{\value{subsection}}% \setcounter{orig@equation}{\value{equation}}% % \def\@tempa{#1}\def\@tempb{section}% \ifx\@tempa\@tempb % reset counter \setcounter{section}{0}% % macro to print original counter \def\theorig@section{\thechapter.\arabic{orig@section}}% % redefine \the... to print the original counter first \def\thesection{\theorig@section\alph{section}}% \else \def\@tempb{subsection}% \ifx\@tempa\@tempb \setcounter{subsection}{0}% \def\theorig@subsection{\thesection.\arabic{orig@subsection}}% \def\thesubsection{\theorig@subsection\alph{subsection}}% \fi \fi % \setcounter{equation}{0}% \def\theorig@equation{\thechapter.\arabic{orig@equation}}% \def\theequation{\theorig@equation\alph{equation}}% % optional \color{blue}% just for testing \noindent\textbf{Addendum: #2}\par \medskip\hrule\medskip\par\noindent \ignorespaces% needed to get rid of the space introduced by \begin{addendum}{...} }{% % optional \par\medskip\hrule\medskip\par % restore counters \setcounter{section}{\value{orig@section}}% \setcounter{subsection}{\value{orig@subsection}}% \setcounter{equation}{\value{orig@equation}}% \endgroup } \makeatother \begin{document} \chapter{Some Chapter} \section{About some Numbers} Some rambling about numbers. \begin{equation} 4 \ne 5 \end{equation} \begin{addendum}[section]{as sections} \section{Section about four and five} Some rambling about four and five \begin{equation} 4 = 5 \end{equation} \subsection{Subsection about four and five} Some rambling about four and five \begin{equation} 4 = 5 \end{equation} \subsection{Another subsection about four and five} Some rambling about four and five \begin{equation} 4 = 5 \end{equation} \section{Another section about four and five} Some rambling about four and five \begin{equation} 4 = 5 \end{equation} \end{addendum} \section{About something else} Some rambling about other things. \begin{equation} 8 \ne 9 \end{equation} \subsection{More on something else} More rambling about other things. \begin{equation} 12 \ne 15 \end{equation} \begin{addendum}[subsection]{as subsections} \subsection{Subsection about twelve and fivteen} More rambling about other things. \begin{equation} 12 = 15 \end{equation} \subsection{Another subsection about twelve and fivteen} More rambling about other things. \begin{equation} 12 = 15 \end{equation} \end{addendum} \subsection{Even more on something else} Even more rambling about other things. \begin{equation} 20 \ne 21 \end{equation} \begin{addendum}{just new equations} Rambling about these numbers. \begin{equation} 20 = 21 \end{equation} \begin{equation} 20 = 21 \end{equation} \end{addendum} Another equation for other things. \begin{equation} 30 \ne 31 \end{equation} \end{document}
The code works by saving the original counters, resetting them and changing the macros to print them (\the...). The counters are restored at the end of the environment. For sectioning commands, care must be taken to only redefine the counter for the highest sectioning level to be inserted. For this the optional argument is used.
Additional counters can be implemented in a similar way. But be careful to not change a counter resetted by another one to be changed. For example, if support for chapters is added, take care not to change the equation counter for an inserted chapter.
The addendum environment works for the book class. For other classes you may have to adapt it.
\startinsertionand\endinsertion?