Deleting multiple items in a shopping cart efficiently

My boss is insistent we need to build functionality to allow users to delete multiple items out of their shopping cart at once (e.g., checkboxes, with a "Select All" button/link, and "Delete" at the top and bottom of pages).

Currently we have the far more typical "Delete" option at the item/product level.

I've researched dozens of competitor carts and not one offers delete-multiple-items-at-once functionality. Edit: AmazonSupply does this, but at the expense of line-item delete.

I'd love to be able to push back on this and prove it's a bad user experience - but honestly the requestor is so adamant about it it's probably an unwinnable discussion.

Anyway does anyone have examples of good implementations of this functionality? It seems like it's going to add a lot of clutter and visual noise and overall is an atypical implementation. Our site has some "Save for Later" functionality multi-select might be beneficial for, but overall I'm concerned about implementing it as it doesn't seem widely done.

Anyway if anyone has good examples of multi-select delete/save in Shopping Carts -- or compelling articles why that functionality shouldn't be used for me to try to beat the requirement back with any help would be appreciated -- thanks!