clip `plot` but leaving plot marks intact

In this TikZ picture

begin{tikzpicture}
draw (0,0) rectangle (5,5);
draw[color=blue] plot[mark=*] coordinates {(-2,3) (0,1) (2,3) (4,2) (6,4)};
end{tikzpicture}

I would like to clip the blue plot lines to the black rectangle. Of course I can achieve that by adding the clip option to the first draw command:

begin{tikzpicture}
draw[clip] (0,0) rectangle (5,5);
draw[color=blue] plot[mark=*] coordinates {(-2,3) (0,1) (2,3) (4,2) (6,4)};
end{tikzpicture}

However, that leads to the plot mark at the edge to be cut in half. Instead, I would like a plot mark to be clipped (not displayed) either completely if the coordinate lies outside of the clip region, or displayed completely if the coordinate lies inside. The result would be like this:

Is it possible to achieve that with some TikZ trickery (i.e. apart from plotting the lines and marks separately)?

documentclass{standalone}
usepackage{pgfplots}

begin{document}

begin{tikzpicture}
    begin{axis}[
        xmin=0,xmax=5,
        ymin=0,ymax=5,
        axis equal image, axis on top,
        clip marker paths=true, ticks=none]
        addplot+[color=blue,mark=*]
            coordinates {(-2,3) (0,1) (2,3) (4,2) (6,4)};
    end{axis}
end{tikzpicture}

end{document}