Only Repeat Customers Allowed to Purchase Online ?

[newtothishelppl]

My company is  looking for someone to help us create a Shopify website that can: 

1. Allow new customers to only design a custom two-sided product, but not complete purchase until it is approved by one of our team members. Both sides could be stock images we provide, or one side could be custom, the other stock or both sides could be custom. 

2. Only allow existing, verified customers to complete a purchase online.

Is this possible on Shopify?