Modular Schanuel conjecture for the modular j-function

Let $z_{1},\ldots,z_{n}\in\mathbb{H}^{+}$.

Modular Schanuel conjecture.

$$\operatorname{tr.deg.}_{\mathbb{Q}}\mathbb{Q}\left(\mathbf{z},j(\mathbf{z})\right)\geq \dim_{G}(\mathbf{z}\mid\Sigma).$$

The source obtains this simpler formulation by removing the derivatives from MSCD and cites it as a related modular transcendence statement. Its resolution is not given.