  The order of the chiral phase transition of lattice QCD with unimproved
staggered fermions is known to depend on the number of quark flavours, their
masses and the lattice spacing. Previous studies in the literature for $N_f \in
\{ 3,4 \}$ show first-order transitions, which weaken with decreasing lattice
spacing. Here we investigate what happens when lattices are made coarser to
establish contact to the strong coupling region. For $N_f \in \{4,8 \}$ we find
a drastic weakening of the transition when going from $N_{\tau}=4$ to
$N_{\tau}=2$, which is consistent with a second-order chiral transition
reported in the literature for $N_f=4$ in the strong coupling limit. This
implies a non-monotonic behaviour of the critical quark or pseudo-scalar meson
mass, which separates first-order transitions from crossover behaviour, as a
function of lattice spacing.
