Wie zeichne ich mehrere Koordinatensysteme bei einem 3D pgfplot gleichzeitig?

\documentclass[varwidth, margin=2.5pt]{standalone}
\usepackage[ngerman]{babel}

\usepackage{pgfplots}
    \pgfplotsset{compat=1.8}
%   \pgfplotsset{compat=newest}

\begin{document}

\begin{tikzpicture}[>=latex] 
\begin{axis}[
%axis  lines = middle,
title={Betragsfl\"ache ~ $z \mapsto |f(z)| = x^2$},
view={-45}{45}, %view = {azimuth}{elevation} % default: {25}{30}
x dir = reverse,
%extra x axis, 
outer axis line style={ultra thin, lightgray},
inner axis line style={ultra thin, lightgray}, % hat Effekt?
zmin=0, zmax = 19, 
xmajorgrids,
ymajorgrids,
zmajorgrids,
%xlabel={$x$},
%ylabel={$y$},
%zlabel={$z$},
ztick={0,4,...,19},
xticklabels=\empty, 
yticklabels=\empty, 
zticklabels=\empty, 
]
\addplot3[mesh,
draw=black,
domain=-4:4,
very thin,
] {x^2};

% EXTRA Koordinatensystem
\draw[->, thick, shorten >=-2.0cm](axis cs: 0,0,0) -- (axis cs: 0,0,16) node[left, yshift=1.25cm, fill=white]{$|f(z)|$};
\draw[->, thick,](axis cs: -4,0,0) -- (axis cs: 4,0,0) node[very near end, above]{$x$};
\draw[->, thick,](axis cs: 0,4,0) -- (axis cs: 0,-4,0) node[very near end, below, xshift=-1.5em, yshift=-0.5em]{$y$};

\end{axis}
\end{tikzpicture}

\end{document}