  We show that the ball does not maximize the first nonzero Steklov eigenvalue
among all contractible domains of fixed boundary volume in $\mathbb{R}^n$ when
$n \geq 3$. This is in contrast to the situation when $n=2$, where a result of
Weinstock from 1954 shows that the disk uniquely maximizes the first Steklov
eigenvalue among all simply connected domains in the plane having the same
boundary length. When $n \geq 3$, we show that increasing the number of
boundary components does not increase the normalized (by boundary volume) first
Steklov eigenvalue. This is in contrast to recent results which have been
obtained for surfaces.
