A major current goal for noncommutative projective geometers is the classification of so-called “noncommutative surfaces”. Let \(S\) denote the \(3\)-dimensional Sklyanin algebra, then \(S\) can be thought of as the generic noncommutative surface. In recent work Rogalski, Sierra and Stafford have begun a project to classify all algebras birational to \(S\). They successfully classify the maximal orders of the \(3\)-Veronese subring \(T\) of \(S\). These maximal orders can be considered as blowups at (possibly non-effective) divisors on the elliptic curve \(E\) associated to \(S\). We are able to obtain similar results in the whole of \(S\).