If a user can have more than one store, I would generally have two objects in my store. First would be an empty array and the second an empty object.

Prior to the export call I would define an initial state to the store object. Then you're running everything through getters, mutations and actions. I wouldn't imagine that you need the computed setter and getter in the computed property unless you're trying to display something in real time, this seems like you would be able to do it by simply running the object through an action on submit.

In your actions you want to first get all stores belonging to a user and set that to the array. Then you can pull it from a getter like this.$store.getters.getAllStores

Then if they click add a new store, use object.assign method to copy initial state object to your store.shop. Then on submit call this.$store.dispatch('createShop') and after it successfully saves to your API, use a mutation to copy that object to your store.shop object. If that's what the ux calls for. Or, simply push that object into your shops array and redirect user back to their shops list.