  We perform a complete classification of two-band $\bk\cdot\mathbf{p}$
theories at band crossing points in 3D semimetals with $n$-fold rotation
symmetry and broken time-reversal symmetry. Using this classification, we show
the existence of new 3D topological semimetals characterized by
$C_{4,6}$-protected double-Weyl nodes with quadratic in-plane (along $k_{x,y}$)
dispersion or $C_6$-protected triple-Weyl nodes with cubic in-plane dispersion.
We apply this theory to the 3D ferromagnet HgCr$_2$Se$_4$ and confirm it is a
double-Weyl metal protected by $C_4$ symmetry. Furthermore, if the direction of
the ferromagnetism is shifted away from the [001]- to the [111]-axis, the
double-Weyl node splits into four single Weyl nodes, as dictated by the point
group $S_6$ of that phase. Finally, we discuss experimentally relevant effects
including splitting of multi-Weyl nodes by applying $C_n$ breaking strain and
the surface Fermi arcs in these new semimetals.
