Can I charge shipping for every item in the cart instead of once per order?

Yes. In the Shipping Zone plugin, a Flat rate method can charge per item:

1. Go to Plugins → Shipping Zone and click Edit on the zone.
2. Under Shipping methods, click + Add method and keep Type as Flat rate.
3. Enter the amount per item in Cost.
4. Tick Charge per item.
5. Enter a Label and click Save zone.

Shipping is then the cost times the total number of items in the cart. For example, 40 per item with three items costs 120.