What you need for this is our premium add-on ATUM Multi-Inventory. With this add-on you will be able to create as many inventories as you want (stores) for a single product. If you enable Selectable Inventories option (list mode) the customer will be able to choose the shop from he/she wants to buy the product.
This is the API documentation: https://stockmanagementlabs.github.io/atum-rest-api-docs/#introduction
In any case, I leave you here the documentation of the add-on where you will find useful info about how the add-on works: https://forum.stockmanagementlabs.com/t/atum-documentation
And the link to the demo site in case you want to try the free trial: https://www.stockmanagementlabs.com/addons/atum-multi-inventory/
Hope this helps,