The NonManifoldMerge tool can be used to combine several manifold or non-manifold* surfaces or polysurfaces into a single non-manifold polysurface. It is a built-in Rhino command but is provided in the Griddle toolbar for convenience as it is useful when operating with Rhino surfaces from which surface and volume meshes will be created.
Triangulating and meshing a polysurface merged with NonmanifoldMerge provides fully conformal nonmanifold mesh with all parts of the mesh being properly attached, as opposed to the case of meshing multiple surfaces separately. At this stage the mesh is ready for remeshing with GSurf with no need to use surface mesh intersector. The advantage to this approach is that it avoids problems related to using improper tolerances during the mesh intersection (GInt) and provides accurate results faster. However, a drawback is that the output surface mesh is now a single complex nonmanifold object (it can be split into pieces using GExtract).
*Edges of polysurfaces or meshes that have more than two faces joined to a single edge are non-manifold (McNeel, 2015).