In my understanding you want a two ordinate plot. The pgfplots manual suggests drawing two axis in one:
\documentclass{book}
\usepackage{pgfplots}
\pgfplotsset{compat=newest}
\begin{document}
\begin{tikzpicture}
\begin{axis}[ scale only axis, xmin=0,xmax=12, axis y line*=left, xlabel=x, ylabel=Small Axis (green)]
\addplot[green] coordinates {(0,0)
(1,0.03)(2,0.04)
(3,0.06)(4,0.7)
(5,1.1)(6,1.4)
(7,1.5)(8,1.2)
(9,0.8)(10,0.5)
(11,0.3)(12,0.1)};
\end{axis}
%
\begin{axis}[ scale only axis, xmin=0,xmax=12, axis y line*=right, axis x line=none, ylabel=Second ordinate (blue)]%
\addplot[blue] coordinates {(0,0)
(1,2)(2,3)
(3,4)(4,6)
(5,11)(6,20)
(7,15)(8,12)
(9,8)(10,7)
(11,3)(12,0)};
%
\addplot[blue] coordinates {(0,4)
(1,6)(2,8)
(3,9)(4,13)
(5,18)(6,29)
(7,50)(8,32)
(9,38)(10,27)
(11,23)(12,10)};
\end{axis}
\end{tikzpicture}
\end{document}

Remark: one should be very carefull with this kind of figures. You have to tell your readers very explicitly that those three curves are not in the same scale. Readers can easily get confused. Although such drawings are quite common in engineering reference books i would not recommend to use that in an educational context nor a paper.
Update In order to draw three lines we need to shift the axis manually. The resulting code is quite a mess but it seems to work. It should be possible to draw even more than 3 axis in this way. You ´ll find your first and second data lining exactly on top of each other. Dataset number one is drawn anyway.
\documentclass{book}
\usepackage{pgfplots}
\pgfplotsset{compat=newest}
\begin{document}
\begin{tikzpicture}
\pgfplotsset{every axis/.style={ymin=0}}
\begin{axis}[ scale only axis, xmin=0,xmax=12, axis y line*=left, xlabel=fractions, ylabel=Small Axis (green)]
\addplot[green, mark=o, draw] coordinates {(0,0)
(1,0.03)(2,0.04)
(3,0.06)(4,0.7)
(5,1.1)(6,1.4)
(7,1.5)(8,1.2)
(9,0.8)(10,0.5)
(11,0.3)(12,0.1)};
\end{axis}
%
\begin{axis}[ scale only axis, xmin=0,xmax=12, axis y line*=right, axis x line=none, ylabel=Second ordinate (blue)]%
\addplot[blue, mark=x] coordinates {(0,0)
(1,2)(2,3)
(3,4)(4,6)
(5,11)(6,20)
(7,15)(8,12)
(9,8)(10,7)
(11,3)(12,0)};
%
\end{axis}
%
\begin{axis}[red, scale only axis, xmin=0,xmax=12, axis y line*=right, axis x line=none, ylabel=third ordinate (red)]%
\pgfplotsset{every outer y axis line/.style={xshift=2cm}, every tick/.style={xshift=2cm}, every y tick label/.style={xshift=2cm} }
\addplot[red ,mark=+] coordinates {(0,4)
(1,6)(2,8)
(3,9)(4,13)
(5,18)(6,29)
(7,50)(8,32)
(9,38)(10,27)
(11,23)(12,10)};
\end{axis}
\end{tikzpicture}
\end{document}

One last remark: as Christian Feuersänger tell us in the pgfplots documentation pgfplots has no idea whats going on. So i suggest that you check your plots made in such a way for errors.
Edit I added ymin to force zeros on the same line.
{}). – Claudio Fiandrino Jul 05 '12 at 13:14