Third Party POS (The Tuna Group) & Wix

I am trying to build a website for a grocery store, but their POS is a third party - The Tuna Group. Their scales are all connected and the grocery outlet is not willing to give it up. Can this be connected to Wix? The backend is coded through this third party which includes the website, but I am discovering that the website is a small piece to the puzzle when it comes to the backend.

Their current website is outdated, BUT has so many layers of purchasing - from grocery to catering and it is all connected to this third party that also created their website.

My thoughts are to keep their backend running and connecting the POS through links, but not sure how to make that possible if we do convert their website, their domain will go with the new site.