Indent every \subsubsection element

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}

\documentclass{article}
\usepackage{lipsum}
\makeatletter
\renewcommand\section{\leftskip 0pt\@startsection {section}{1}{\z@}%
                                   {-3.5ex \@plus -1ex \@minus -.2ex}%
                                   {2.3ex \@plus.2ex}%
                                   {\normalfont\Large\bfseries}}
\renewcommand\subsection{\leftskip 0pt\@startsection{subsection}{2}{\z@}%
                                     {-3.25ex\@plus -1ex \@minus -.2ex}%
                                     {1.5ex \@plus .2ex}%
                                     {\normalfont\large\bfseries}}
\newcommand\Xsubsubsection{\@startsection{subsubsection}{3}{\z@}%
                                     {-3.25ex\@plus -1ex \@minus -.2ex}%
                                     {1.5ex \@plus .2ex}%
                                     {\normalfont\normalsize\bfseries\leftskip 3ex}}
\renewcommand\subsubsection[1]{\Xsubsubsection{#1}\leftskip 3ex}
\makeatother
\begin{document}
\section{My section}

\lipsum[4]

\subsection{My subsection}

\lipsum[4]

\subsubsection{My subsubsection\label{xxx}}

In subsection \ref{xxx}, we have the indent.

\subsection{Next subsection}

\lipsum[4]

\section{next section}

\lipsum[4]
\end{document}