In the new breakpoint, where you need an entirely new menu, right-click on all the aspects of the menu (Menu Widget, Menu Container, Close Button, Menu Trigger) and select "Hide in breakpoint"
Place a new copy of the widget from the Library panel into the page, or copy/paste all the aspects of the menu (Menu Widget, Menu Container, Close Button, Menu Trigger) from another breakpoint into the new breakpoint.
Now you have a breakpoint that has a new copy of the menu, but you need o hide this new copy from other breakpoints. So go to every other breakpoint and you will see two copies of the menu; the original one and the one you just placed in the new breakpoint, so you need to right-click and "Hide in Breakpoint" the new copy in all the breakpoints except in the one you want the new copy in it.
The idea is to get a new copy of the menu only in the breakpoint/s that in which you want a different menu, but keep the original one in the other ones.
Now you can style the new copy of the menu and you will have the option to change every aspects of it, such as position and the entire content.