Building integration to Shopify from SaaS platform

[timinc]

I'm working with my developer who is building his first integration to Shopify.

We used to have a private app (now converted to a custom app) that required the user to give us all of their credentials. That required every customer to install an app on the Shopify admin account just to get the credentials.  It was really confusing for people to leave our app, to go and get these credentials and come back and paste them in.

We're in the process of completing a new login flow on our own platform in which we want the user to simply select Shopify as an integration, have them go through an OAuth process just like they would with Facebook, DropBox, Zoom, any 3rd party app.  In each of those examples, I create a single, private app that everyone uses.

So our question is, can we build this using a single custom app, have each user on our platform using our login flow enter the store name, have have the OAuth dialog popup, go through and get the access token we need? We want to avoid having our user have to leave our log in flow, install an app over on Shopify and then come back to make all of this work.  

Currently we installed the app on our dev store and have been using the credentials from that to invoke the OAuth process.  We've found that the only missing thing is the store name which I guess we could prompt the user to manually enter (not ideal).  It would be better if we had some way to prompt the user to log into Shopify during our login flow to get the store name.  That's how Facebook OAuth works.  As long as I have an active logged session, the OAuth process picks up what you need from that and if not, it prompts me to log in.  That's basically the way we are looking for Shopify OAuth to work.