  A famous result about mass partitions is the so called \emph{Ham-Sandwich
theorem}. It states that any $d$ mass distributions in $\mathbb{R}^d$ can be
simultaneously bisected by a single hyperplane. In this work, we study two
related questions.
  The first one is how many masses we can simultaneously partition with a
$k$-fan, that is, $k$ half-hyperplanes in $\mathbb{R}^d$, emanating from a
common $(d-2)$-dimensional apex. This question was extensively studied in the
plane, but in higher dimensions the only known results are for the case where
$k$ is an odd prime. We extend these results to a larger family of values of
$k$. We further present a new result for $k=2$, which generalizes to cones.
  The second question considers bisections with double wedges or, equivalently,
Ham-Sandwich cuts after projective transformations. Here we prove that given
$d$ families of $d+1$ point sets each, there is always a projective
transformation such that after the transformation, each family has a
Ham-Sandwich cut. We further prove a result on partitions with parallel
hyperplanes after a projective transformation.
