How to add another row of tick labels?

Question

Rather than adding a second x axis by putting it on the other side of the plot I would like to add one implicitly simply by adding another row of tick labels to an existing axis. What I am after is something like the following mockup:

Using the idea in this answer I have tried to come up with something like this but there are some problems and maybe there is a better approach to the issue?

\documentclass{article}

\usepackage{pgfplots}

\pgfplotsset{
      domain=0:1,
      xmin=0, xmax=1,
      ymax=1, ymin=0
    }

\begin{document}

\begin{figure}
  \begin{tikzpicture}
    \begin{axis}[xtick align=inside,
      extra x ticks={0.2, 0.4, ..., 0.8},
      extra x tick labels={0.33, 0.33, 0.33, 0.33},
      every extra x tick/.style={
        xtick align=outside,
      },
      xlabel=\(x_1\),
      after end axis/.code={
        \node  at (rel axis cs:1,0) [anchor=south west, align=left] {\(x_2\)};
      }
      ]
      \addplot{x};
    \end{axis}
  \end{tikzpicture}
\end{figure}

\end{document}

Answer 1

Using major tick length=0pt for the every extra x tick style, you can get rid of the ticks for the extra labels; you can prevent the overlapping using a yshift; using the axis description coordinate system you can place \(x_1\) and \(x_2\):

\documentclass{article}
\usepackage{pgfplots}

\pgfplotsset{
      domain=0:1,
      xmin=0, xmax=1,
      ymax=1, ymin=0
    }

\begin{document}

\begin{figure}
  \begin{tikzpicture}
    \begin{axis}[xtick align=inside,clip=false,
      extra x ticks={0, 0.2, 0.4, ..., 1},
      extra x tick labels={0.33, 0.33, 0.33, 0.33, 0.33,0.33},
      every extra x tick/.style={major tick length=0pt,
        xtick align=outside,yshift=-10pt}
      ]
      \addplot{x};
        \node  at (axis description cs:0,0) [anchor=north east, align=left,xshift=-12pt] {\(x_1\)};
        \node  at (axis description cs:0,0) [anchor=north east, align=left,xshift=-12pt,yshift=-11pt] {\(x_2\)};
    \end{axis}

  \end{tikzpicture}
\end{figure}

\end{document}