  We determine the maximal non-central hyperplane sections of the n-dimensional
$l_1$-ball if the fixed distance of the hyperplane to the origin is between $1
/ \sqrt 3$ and $1 / \sqrt 2$. This adds to a result of Liu and Tkocz who
considered the distance range between $1 / \sqrt 2$ and 1. For $n > 3$, the
maximal sections are parallel to the $(n-1)$-dimensional coordinate planes. We
also study non-central sections of the complex $l_1^2$- and $l_\infty^2$-balls,
where the formulas are more complicated than in the real case. Also, the
extrema are partially different than in the real case.
