We explore the landscape of F-theory compactifications on Calabi-Yau fourfolds whose complex structure moduli space is the thrice-punctured sphere. As a first part, we enumerate all such Calabi-Yau fourfolds under the additional requirement that it has a large complex structure and conifold point at two of the punctures. We find 14 monodromy tuples by demanding the monodromy around infinity to be quasi-unipotent. As second part, we study the four different types of phases arising at infinity. For each we consider a working example where we determine the leading periods and other physical couplings. We also included a notebook that sets up the period vectors for any of these models.