My proposal is just to use \part
s in order to separate your document in parts such as "Main Part", "Appendices" etc
Here is how:
\documentclass[12pt, a4paper,oneside,article]{memoir}
%Simplified solution for spacing after part number from:
% https://tex.stackexchange.com/a/467235/120578
\makeatletter
\renewcommand\partnumberlinehook[1]{%
\setlength{\@tempdima}{2em}%
}
\makeatother
\title{title}
\author{Some Author}
\begin{document}
\frontmatter
\maketitle
\tableofcontents
\clearpage
\begin{abstract}
Some abstract
\end{abstract}
\mainmatter
\part{Main Part}
\chapter{First Chapter}
\section{One section}
\section{Another Section}
\chapter{Second Chapter}
\section{A section of second Chapter}
\section{Another section of second chapter}
\appendix
\part{Appendix I}
\chapter{First Appendix I Chapter}
\chapter{Second Appendix I Chapter}
\part{Appendix II}
\chapter{First Appendix II Chapter}
\chapter{Second Appendix II Chapter}
\end{document}
Then, you could use the chapter numbers to be inside the part like
\renewcommand{\thechapter}{\thepart.\Alph{chapter}}
and also could set the chapter counter to zero at every part begin like:
\part{Appendix II}
\setcounter{chapter}{0}
\chapter{First Appendix II Chapter}
etc
Full example:
\documentclass[12pt, a4paper,oneside,article]{memoir}
%Simplified solution for spacing after part number from:
% https://tex.stackexchange.com/a/467235/120578
\makeatletter
\renewcommand\partnumberlinehook[1]{%
\setlength{\@tempdima}{2em}%
}
\renewcommand\chapternumberlinehook[1]{%
\setlength{\@tempdima}{3em}
}
\makeatother
\title{title}
\author{Some Author}
\begin{document}
\frontmatter
\maketitle
\tableofcontents
\clearpage
\begin{abstract}
Some abstract
\end{abstract}
\mainmatter
\part{Main Part}
\chapter{First Chapter}
\section{One section}
\section{Another Section}
\chapter{Second Chapter}
\section{A section of second Chapter}
\section{Another section of second chapter}
\appendix
\renewcommand{\thechapter}{\thepart.\Alph{chapter}}
\part{Appendix I}
\chapter{First Appendix I Chapter}
\chapter{Second Appendix I Chapter}
\part{Appendix II}
\setcounter{chapter}{0}
\chapter{First Appendix II Chapter}
\chapter{Second Appendix II Chapter}
\end{document}
That gives:
But is you insist in your request, this could solve your problem:
\documentclass[12pt, a4paper,oneside,article]{memoir}
\title{title}
\author{Some Author}
\begin{document}
\frontmatter
\maketitle
\tableofcontents
\clearpage
\begin{abstract}
Some abstract
\end{abstract}
\mainmatter
\chapter{First Chapter}
\section{One section}
\section{Another Section}
\chapter{Second Chapter}
\section{A section of second Chapter}
\section{Another section of second chapter}
\clearpage
\appendix
\chapter*{Appendix I}\addcontentsline{toc}{chapter}{Appendix}
\renewcommand{\thesection}{\Alph{section}}
\section{First Section of Appendix }
\section{Second Appendix}
\end{document}