Another solution is to use two multi-value fields to accomplish this. One multi-value field to Add Line Item Amounts, and the other to store Previously-Added Line Item Amounts. The Previously-Added Line Item Amounts field would be read-only.

When a manager wants to add one or more line item amounts they would type into the Add Line Item Amounts multi-value field. A workflow would then be set up to monitor any addition of values to that field. If a value is added, Workflow could take that value and added it to the other field, which is read-only for the managers but accessible to Workflow. It could also add information such manager's name if desired, to keep a record of who added what amounts. Workflow would then clear out the values in the Add Line Item Amounts field, so that it's an empty field for the next manager to add values to. 

This setup essentially provides one field to add new values that will be cleared after every new addition, and a second field to keep a read-only history of all values that have been added.