This is my solution Crab Sync, and I hope it can help you. Please feel free to contact me if you have any questions.
Topic summary
Sharing one inventory across multiple Shopify storefronts (different domains/designs) is possible via third‑party apps; Shopify Support recommended Syncio Multi Store Sync, Multi-Store Sync Power, and InventorySync, and advised contacting each developer for specifics.
Trunk was highlighted for real-time syncing across multiple Shopify stores, building a centralized inventory and updating stock on sales or manual changes. It requires matching SKUs (stock-keeping units) across stores and supports bundles/kits; a corrected help link was provided.
A merchant asked about creating a single B2B/wholesale site aggregating products from four B2C Shopify stores (plus extras) and whether a new site is needed. Support redirected to app developers; no clear solution was confirmed, and a follow-up indicated it remains unresolved.
Cost concerns were raised for smaller stores, while others endorsed Trunk. Additional options promoted: Sync Master Gogo (pay-as-you-grow pricing, multi-location and multi-store syncing, SKU-based or manual product grouping) and Crab Sync.
Outstanding question: whether these apps can prevent overselling with simultaneous orders across stores. This was not answered, and the thread remains open with no final decision.