“Anything more?”  or “Any more”  are commonly uttered by enthusiastic sales assistants or cashiers.

Perhaps the intention is to find out:

• if there are other items that the customer may want
  
  
• to remind them to think about what they may have forgotten to buy.

In any case, “Anymore”  and “Anything more”  is vague and not very useful.

Ask Your Questions Correctly

If you are asking so that you can help your customer look for more items that they want, then it’s better to say:

• “Would you like to get anything else?
  
  
• “Can I help you get anything else?”

If you want to remind them to check that they’ve gotten all the items they need, then you should say: “Is that all the items on your shopping list? Let me know if there is anything else that I can help you with?”

Source: Edited from the Singapore Retailers Association's Speak Good English pamphlet.