  We analyze the role of maximally aligned isoscalar pairs in heavy $N=Z$
nuclei by employing a formalism of quartets. Quartets are superpositions of two
neutrons and two protons coupled to total isospin $T=0$ and given $J$. The
study is focused on the contribution of spin-aligned pairs carrying the angular
momentum $J=9$ to the structure of $^{96}$Cd and $^{92}$Pd. We show that the
role played by the $J=9$ pairs is quite sensitive to the model space and, in
particular, it decreases considerably by passing from the simple $0g_{9/2}$
space to the more complete $1p_{1/2}$,$1p_{3/2}$,$0f_{5/2}$,$0g_{9/2}$ space.
In the latter case the description of these nuclei in terms of only
spin-aligned $J=9$ pairs turns out to be unsatisfactory while an important
contribution, particularly in the ground state, is seen to arise from isovector
$J=0$ and isoscalar $J=1$ pairs. Thus, contrary to previous studies, we find no
compelling evidence of a spin-aligned pairing phase in $^{92}$Pd.
