Aria here, I'm on the Social Care team at Shopify. ?
Can you please tell me what it is you like about the ASOS theme? Keep in mind, they won't have used an off the shelf theme, they will have customized it to get it the way it is now. If I have an understanding of the features you're looking for, I can recommend themes and apps to help you achieve them. You can also consider using a Shopify Expert to build something custom for you.
I'll look out for your response.
Social Care Guru