Hi Data Science Stack Exchange! I'm new here but I'm familiar with some machine learning theory (took some courses in school) and my question is more about how to apply ML in a practical setting.

I have this project where I'm trying to design a system to predict which "store" a user is going to buy a given item from. However, the set of stores a user can potentially buy from is already known for each user (because this promotion only works at limited stores they signed up for). On average, the set of stores the average user can buy from is around 3 but the # of distinct stores across all users is about 10000.

In theory, for a single user this seems like a simple classification problem. We have historical information such as the time/day/month the user bought item Y from store X along with other features such as location (postal code) where the user lives and features related to the type of item they are buying (cost, weight, brand).

However, the issue is that there's currently around 6000 users so going with this approach seems like I would need a separate model for each user but that doesn't seem like an efficient solution to me or at least not how I've generally seen ML algorithms used. Unfortunately, I don't see any other way I could take into account the fact that the set of stores a user can already buy from is known for each user already. I suppose I could have a categorical variable for each buy-able store as a feature but then that would be equivalent to adding 10000 features and I'm not sure if this would scale as the number of distinct stores increases.

It would be really helpful if anyone has any insight on how to apply machine learning techniques to this kind of problem in general as this is sort my first time working on a "real" problem. Thanks!