  In this paper, we consider higher regularity of a weak solution $({\bf u},p)$
to stationary Stokes systems with variable coefficients. Under the assumptions
that coefficients and data are piecewise $C^{s,\delta}$ in a bounded domain
consisting of a finite number of subdomains with interfacial boundaries in
$C^{s+1,\mu}$, where $s$ is a positive integer, $\delta\in (0,1)$, and $\mu\in
(0,1]$, we show that $D{\bf u}$ and $p$ are piecewise $C^{s,\delta_{\mu}}$,
where $\delta_{\mu}=\min\big\{\frac{1}{2},\mu,\delta\big\}$. Our result is new
even in the 2D case with piecewise constant coefficients.
