\documentclass[]{article}
\usepackage{alphalph}
\usepackage{enumitem}
\makeatletter
\def\enumalphalphcnt#1{\expandafter\@enumalphalphcnt\csname c@#1\endcsname}
\def\@enumalphalphcnt#1{\alphalph{#1}}
\makeatother
\AddEnumerateCounter{\enumalphalphcnt}{\@enumalphalphcnt}{aa}
\setenumerate{label=\arabic*}
\setenumerate[2]{label=\enumalphalphcnt*)}
\begin{document}
\begin{enumerate}
\item foo
\item bar
\item next level
\begin{enumerate}
\item foo \item bar \item foo
\item bar \item foo \item bar
\item foo \item bar \item foo
\item bar \item foo \item bar
\item foo \item bar \item foo
\item bar \item foo \item bar
\item foo \item bar \item foo
\item bar \item foo \item bar
\item foo \item bar \item foo
\item bar \item foo \item bar
\item foo \item bar \item foo
\item bar \item foo \item bar
\item foo \item bar \item foo
\item bar \item foo \item bar
\item foo \item bar \item foo
\item bar \item foo \item bar
\end{enumerate}
\end{enumerate}
\end{document}