It all depends on how you implement things.
How do you plan to make the transition / duplication?
I don’t think s2member has native support for single subscriptions that work on 2 sites, but you can probably work things out one way or another, depending on your creativity and the size of your user base.
I personally do many things manually because I have a handful of users (to whom I am very thankful to). That means I can even use payment processors not support by s2member by promoting and demoting users manually and using the existing fields (and the custom capabilities) to hold meaningful information (or I add extra ones, as needed).
If a new user creates a new subscription using an s2member form or button, it will create one subscription.
If they use a button or form to upgrade, same.
Unless you duplicate your existing subscriptions on Stripe and you have the setting that allows for more than a subscription per user turned on, they should be blocked from having multiple ones on Stripe’s end.
On the other hand, if you want that possibility open (multiple subscriptions per user) you need to turn that feature off.
If a user creates a new subscription on one site, it won’t automatically propagate to the other via s2member routines (as far as I am aware of). There’s also a custom field with your domain name that will prevent s2member to act if that does not match. You’ll need to make modifications to be able to use those, including keeping your wordpress user database current with the latest payments, cancellations, declines etc.
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