  We prove the Zilber--Pink conjecture for curves in $Y(1)^n$ whose Zariski
closure in $(\mathbb{P}^1)^n$ passes through the point $(\infty, \ldots,
\infty)$, going beyond the asymmetry condition of Habegger and Pila. Our proof
is based on a height bound following Andr\'e's G-functions method. The
principal novelty is that we exploit relations between evaluations of
G-functions at unboundedly many non-archimedean places.
