I will outline a general strategy for studying Morita equivalences of Lie groupoids with additional geometry. Along the way we will briefly review the site theoretic definition of a geometric stack as well as the main theorems which relate them to groupoids. We will see that by replacing the site of smooth manifolds, one can sometimes obtain a rigorous notion of the 'geometric stack' associated to a groupoid with geometry. We will give at least one example where this strategy has already been successful, symplectic groupoids.