I doubt that the line-item veto is a good example, because there are so many complications in any kind of real politics. For example, C&C might agree in advance that a certain line item will be included only if some other item is not vetoed. This improves everyone's utility without going all the way back to the "all-or-nothing" setup, in essence prioritizing the line items.

An example where workarounds are impossible or unlikely would illustrate the standard idea of working backwards better.