You can create menus that are shown for specific membership levels. To do this, you first need to enable custom menus for each of your membership levels that require it.
After you do this, you will see a new menu area whenever you add/edit a WordPress menu (wp-admin->APPEARANCE->MENUS):
When you assign a menu to a membership specific display location, it will display whenever a user with that membership level logs in, completely replacing the standard menu.
Additionally, you have two new display locations that can be used regardless of membership levels: Logged-in Non-Members and Members.
You can use the SPMS menu widget in a side-bar to conditionally show a menu to users of a particular membership level as well as a different menu for logged in members and logged in non-members.
Many plugins and some themes attempt to control menus and these can conflict with our menu logic. If you have multiple plugins attempting to switch menus or conditionally display menus, only one will win. So if you’re seeing any behavior where your menus are not appearing the way you think they should, then check to make sure that another plugin or your theme isn’t trying to exercise control over the menus as well.