I will discuss work in progress with M. Orr (Manchester) and G. Papas (Weizmann) on the Zilber-Pink conjecture for $Y(1)^3$. This is known for so-called asymmetric curves by the 2012 work of Habegger-Pila. More recently, an approach known as the G-function method, has yielded further cases, namely, curves intersecting $(\infty,\infty,\infty)$ (D-Orr) and curves intersecting a special point in the boundary (Papas). In this work, we extend the method to deal with curves intersecting a boundary modular curve, and to give an unconditional result for points with few places of supersingular reduction.