Entangled Suslin lines and OGA

We construct a model of the Open Graph Axiom (OGA) in which there is a 2-entangled Suslin line $S$. Consequently, in this model, there is a 2-entangled uncountable linear order, but no such order is separable. This resolves a problem posed by Carroy, Levine, and Notaro \cite{carroy2025} and answers a question from McKenney on MathOverflow \cite{Mckenney2014}.