Help with finding the right POS System

Hi guys,

I′m having difficulties in finding the right Point of Sale System for us and I was hoping someone might have a similar setup and some experience or recommendations for me.

We are currently running 1 Online Shop and 3 physical stores.
We are working with a decentralized inventory meaning:
Each of them has an inventory, so 1 inventory for the Online Shop at our Business Offices adress, and 3 seperate inventory at the respective adresses of the physical stores. So all 4 inventories are at different physical locations.

We are looking for a reliable, good POS System that can also provide a good inventory management for all 4 inventories but most of all should be able to do the following fullfilment logic:

If someone orders an item in the online store, we would like check

if the item is in the inventory of the online store (business office location), if so start fulfillment/send outs from there and reduce the iventory stock of that inventory,

if not, check if the first physical store has the item in its inventory and then do the fulfilment sendout from that location and reduce the invetory stock of that physical store, and so forth

We were previously using Shopify and it was possible and very easy to do…

Does anyone have a good POS recommendation for that or a combination of a POS and a fullfilment or inventory plugin that is able to work with that POS?

I was looking at the inventory management system from ATUM, which definately has those fulfilment rules/logic you can setup, but couldn′t find a POS to communicate with it.

Thank you so much for your time and help! Much aprreciate it!

Best,
Andi