  Altermagnets are compensated magnets with unconventional $d$, $g$, and
$i$-wave spin order in reciprocal space. So far the search for new
altermagnetic candidates has been focused on materials in which the magnetic
unit cell is identical to the non-magnetic one, i.e. magnetic structures with
zero propagation vector. Here, we substantially broaden the family of
altermagnetic candidates by predicting supercell altermagnets. Their magnetic
unit cell is constructed by enlarging the nonmagnetic primitive unit cell,
resulting in a non-zero propagation vector for the magnetic structure. This
connection of the magnetic configuration to the ordering of sublattices gives
an extra degree of freedom to supercell altermagnets, which can allow for the
control over the order parameter spatial orientation. We identify realistic
candidates MnSe$_2$ with a $d$-wave order, and RbCoBr$_3$, CsCoCr$_3$, and
BaMnO$_3$ with $g$-wave order. We demonstrate the reorientation of the order
parameter in MnSe$_2$, which has two different magnetic configurations, whose
energy difference is only 5 meV, opening the possibility of controlling the
orientation of the altermagnetic order parameter by external perturbations.
