The MSI tool is the method that changes the triangulation of the offset surface, but it is the most useful if you need to offset specific areas (especially if you have different offsets in different areas). This tool is indispensable if you have offsets that you may need to edit later. The offset result is usually pretty high-fidelity although I have encountered quirky behavior a couple of times. I usually create a cut/fill map between the original and offset surfaces. You can map specific colors to the offset values you've used to visually confirm the areas applied, and with "Smooth Transition" turned off in the color map you can maximize detection of offset errors. Also, if you have the "Coordinate Scroll" tool open and the cut/fill isopach selected you get a live reading of the offset under the mouse cursor.
Another way to achieve surface offsets that hasn't been mentioned works similar to the "Explode Surface" macro: you can export your surface to a *.dxf or *.dwg file, and when you re-import it you will find it composed of 3D CAD faces which can be manipulated using the "Change Elevation" and other transform tools. Use the manipulated faces as members to create a new surface.
-You can manually select the faces within areas of interest and apply specific offsets. I use selection sets or re-layering to sort regions. Note that each triangle edge overlaps any neighboring triangle edges, so simply applying a vertical shift to a subset of the triangles will produce flags along these edges; use the "Shrink3DFaces" command to eliminate this overlap.
-Another thing you can do is use the "Convert to Linestring" macro to change these faces into normal linestrings which can then be edited in all the normal ways.