pgfplots fillbetween with multiple curves

Question

I have a TikZ picture like this:

\begin{tikzpicture}
  \begin{axis}[
    axis lines=middle,
    xmin=-0.5,xmax=3.5,ymin=-0.5,ymax=3.5
  ]
  \addplot[very thick,blue, samples=300, domain=0:3, name path=A] {sqrt(x)}; 
  \addplot[very thick,yellow!70!red, samples=300, domain=0:3, name path=B] {9-3*x}; 
  \addplot[very thick,red!90!teal, samples=300, domain=0:3, name path=C] {3}; 
  \addplot[very thick,green!70!magenta, samples=300, domain=0:3, name path=D] coordinates{(1/9,-6) (1/9,6)};
  \end{axis}
\end{tikzpicture}

I’d like to fill the area enclosed by these four curves.

Similar questions have been answered using pgfplots’s fillbetween package, but it only seems to support filling between two curves. What are my options?

Answer 1

Here a workaround, you can divide your area on two parts: first between curve A and C, and the second between A and B and use soft clip to limit filling

\documentclass[border=5mm]{standalone}
\usepackage{pgfplots}
\usepgfplotslibrary{fillbetween}
\begin{document}

\begin{tikzpicture}
  \begin{axis}[
    axis lines=middle,
    xmin=-0.5,xmax=3.5,ymin=-0.5,ymax=3.5
  ]
  \addplot[very thick,blue, samples=300, domain=0:3, name path=A] {sqrt(x)}; 
  \addplot[very thick,yellow!70!red, samples=300, domain=0:3, name path=B] {9-3*x}; 
  \addplot[very thick,red!90!teal, samples=300, domain=0:3, name path=C] {3}; 
  \addplot[very thick,green!70!magenta, samples=300, domain=0:3, name path=D] coordinates{(1/9,-6) (1/9,6)};
  \addplot[gray!30] fill between[of=A and C,soft clip={domain=1/9:2}];
  \addplot[gray!30] fill between[of=A and B,soft clip={domain=2:2.5}];
  \end{axis}
\end{tikzpicture}

\end{document}