No, you cannot have multiple Zamplebox subscriptions you are allowed to have one subscription per account.
However, you are allowed to have an ABAY OR ZBGO auto-ship subscription on your account while having an active box subscription. Below are examples of how these subscriptions look on your member's dashboard
Regular Zamplebox Box Subscription:
ATTENTION: Please keep in mind that each subscription is individual meaning that just because you change your renewal date on your ABAY subscription this does not mean that your renewal date on your regular box subscription will be updated, each one must be done individually using the little drop-down arrow on the right.