Static Menu Button

[gwpriester]

The menu for the main site and the variant is a repeating object and will be in the same position on all pages. Unless you right click on the menu bar and select Stop Repeating. So I think the answer to your question is the menu is already static.

I created a simple three page site with a variant so you can see how it works.

If you move or edit the button on the variant, the other buttons will move and/or resize.