Sorry, but I don't see any easy way to get around the issue... Is it possible to move the geometry that can be enabled / disabled to another vertex buffer - or even to a special portion of the vertex buffer that would help you keep the indices manageable?
If the plane pieces are normally the same size, you could also try using instancing to render the expandable parts. When thickness is disabled, you render using a thin plane as your per vertex data, and when it is enabled, you could switch the data to include the thicker version. That would actually work out pretty easy I think... Does that sound possible?
I figured out with this by adding extra points in the end of my vertexBuffer and build 2 indexbuffers: first without additional points - normal model, second with additional points - thick figures. Using ON/OFF thickness I'm just changing index buffers and render model.
Thanks for help Jason!