You can use the style more than once:
\node [draw, double circle={2pt}{black!75},
double circle={4pt}{black!50},
double circle={6pt}{black!25}] (c1) {};
Or could nest them:
\node [draw,
double circle={2pt}{black!75,
double circle={2pt}{black!50,
double circle={2pt}{black!25}}}] (c1) {};
Code
\documentclass[tikz] {standalone}
\usetikzlibrary{calc}
\tikzset{
old inner xsep/.estore in=\oldinnerxsep,
old inner ysep/.estore in=\oldinnerysep,
double circle/.style 2 args={
circle,
old inner xsep=\pgfkeysvalueof{/pgf/inner xsep},
old inner ysep=\pgfkeysvalueof{/pgf/inner ysep},
/pgf/inner xsep=\oldinnerxsep+#1,
/pgf/inner ysep=\oldinnerysep+#1,
alias=sourcenode,
append after command={
let \p1 = (sourcenode.center),
\p2 = (sourcenode.east),
\n1 = {\x2-\x1-#1-0.5*\pgflinewidth}
in
node [inner sep=0pt, draw, circle, minimum width=2*\n1,at=(\p1),#2] {}
}
},
double circle/.default={2pt}{blue}
}
\begin{document}
\begin{tikzpicture}
\node [draw, double circle={2pt}{black!75},
double circle={4pt}{black!50},
double circle={6pt}{black!25}] (c1) {};
\node [draw, double circle={-2pt}{black!75},
double circle={-4pt}{black!50},
double circle={-6pt}{black!25}] (c2) at (2,0) {};
\end{tikzpicture}
\begin{tikzpicture}
\node [draw,
double circle={2pt}{black!75,
double circle={2pt}{black!50,
double circle={2pt}{black!25}}}] (c1) {};
\node [draw,
double circle={-2pt}{black!75,
double circle={-2pt}{black!50,
double circle={-2pt}{black!25}}}] (c2) at (2,0) {};
\end{tikzpicture}
Output

