  We study the shape coexistence of differently deformed states within
$^{28}$Si using shell-model and beyond-mean-field techniques. Experimentally,
$^{28}$Si exhibits shape coexistence between an oblate ground state and an
excited prolate structure. The oblate rotational band is described well within
the $sd$ shell using the USDB interaction. However, for the prolate band, a
modification of this interaction is required, lowering the single-particle
energy of the $1d_{3/2}$ orbit. Furthermore, we explore the possibility of a
superdeformed configuration in $^{28}$Si. Our calculations, spanning both the
$sd$ and $pf$ shells, rule out the existence of a superdeformed $0^+$ bandhead
within an excitation energy range of 10-20 MeV.
