  We study the vacua of $4d$ heterotic toroidal orbifolds using effective
theories consisting of an overall K\"{a}hler modulus, the dilaton, and
non-perturbative corrections to both the superpotential and K\"{a}hler
potential that respect modular invariance. We prove three de Sitter no-go
theorems for several classes of vacua and thereby substantiate and extend
previous conjectures. Additionally, we provide evidence that extrema of the
scalar potential can occur inside the PSL$(2,\mathbb{Z})$ fundamental domain of
the K\"{a}hler modulus, in contradiction of a separate conjecture. We also
illustrate a loophole in the no-go theorems and determine criteria that allow
for metastable de Sitter vacua. Finally, we identify inherently stringy
non-perturbative effects in the dilaton sector that could exploit this loophole
and potentially realize de Sitter vacua
