  We provide a description of deformed $N=Z$ nuclei in a formalism of
$\alpha$-like quartets. Quartets are constructed variationally by resorting to
the use of proper intrinsic states. Various types of intrinsic states are
introduced which generate different sets of quartets for a given nucleus.
Energy spectra are generated via configuration-iteraction calculations in the
spaces built with these quartets. The approach has been applied to $^{24}$Mg
and $^{28}$Si in the $sd$ shell and to $^{48}$Cr in the $pf$ shell. In all
cases a good description of the low-lying spectra has been achieved. As a
peculiarity of the approach, a close correspondence is observed between the
various sets of quartets employed and the occurrence of well defined band-like
structures in the spectra of the systems under study.
