This is more the config on JAT3 framework and JA Community Plus Template. I would like to clarify that for heavy customization, you should hire a developer to carry out such work, customization support is out of JA support scope.
If you are a developer you can try to do with my below solution
+ Go Admin site -> Menus -> Create new for mobile / iPhone
+ Go to Admin of JA Community Plus template
+ Create new profile on PROFILES tab
+ Appear new profile with Menu Type and Create new menu for mobile / iPhone
+ In Language & Page Assignments on JA Community Plus Template and assing menu item with new this profile