The result is awful and I can see no reason for wanting this. But the document is yours.
\documentclass{article}
\usepackage{changepage}
\usepackage{lipsum} % just for the example
\newenvironment{subs}
{\adjustwidth{3em}{0pt}}
{\endadjustwidth}
\begin{document}
\section{A section}
\lipsum[1]
\subsection{A subsection}
\lipsum[2]
\begin{subs}
\subsubsection{One}
\lipsum[3]
\subsubsection{Two}
\lipsum[4]
\end{subs}
\lipsum[5]
\end{document}

With the following change, the subsubsection titles will be flush with the left margin. The result is even more awful than before.
\documentclass{article}
\usepackage{changepage}
\usepackage{lipsum} % just for the example
\newenvironment{subs}
{\adjustwidth{2pc}{0pt}}
{\endadjustwidth}
\makeatletter
\renewcommand\subsubsection{%
\@startsection{subsubsection}{3}
{-2pc}% <------- The opposite of what we set for subs
{-3.25ex\@plus -1ex \@minus -.2ex}%
{1.5ex \@plus .2ex}%
{\normalfont\normalsize\bfseries}}
\makeatother
\begin{document}
\section{A section}
\lipsum[1]
\subsection{A subsection}
\lipsum[2]
\begin{subs}
\subsubsection{One}
\lipsum[3]
\subsubsection{Two}
\lipsum[4]
\end{subs}
\lipsum[5]
\end{document}