Hi,
I don't know what your level of Joomla knowledge is, but it is possible.
The easiest way is to simply add menu items visible only to registered users. Using Joomla Access Levels you can do a lot. Here you use what you already have in CMS box.
But you can also...
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For Joomla 3 was extension "Advanced Template Manager" (RegularLabs) in which you could set different template for different User Groups etc. of course with different menu set inside.
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You can also customize template code and load different menu for logged users. This, however, requires editing the code.
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Do not use our menu from Helix, but create a custom header with logo and position name, for example, "top3" and there publish extra installed MegaMenu module (are available as free/pro). And with module you can do what you want. Even with using Advanced Module Manager (RegularLabs). This 3rd option seems the flexible and simplest to do. Even if you had to spend a few dollars for extra extension(s).
These are free tips I can give you here.