Goal: Show different menus on different pages within one Shopify store (Index uses Main Menu; Shop 1 uses Menu1; Shop 2 uses Menu2). The aim is to avoid multiple accounts and keep all sales under one account.
Advice offered: Create multiple menus in Online Store > Navigation and assign them via theme customization. Use header/primary navigation settings per page where available.
Issue reported: In the Dawn theme, changing a page’s menu in Theme Customize also changes the Home (index) menu. This indicates the header menu setting is global in Dawn. The OP believes custom coding is required but needs guidance.
Related query: Another user on the Origin theme asks how to assign a subcategory menu to a specific collection (e.g., women’s shoes > high heels/running shoes/sandals/casual). They also ask about mobile display and note no third-tier option in their current menu.
Resource shared: A YouTube video demonstrating different navigation per collection was provided.
Status: No confirmed, theme-specific solution in-thread. Likely requires theme customization or code; details remain unresolved and discussion is open.
Hi and thanks for your reply 
Unfortunately the solution is not as easy as you suggest. If you change the Menu in a page while being in the “Theme Customize” (Dawn template) the Menu will also change on the home page (index).
I believe the solution is to do some hard coding in the theme editor. But I do not know where and how.