Dates cannot be edited in a Plan
One answer
Based on the question I am assuming that you are using the Formal process template.
In formal template we have a scheduler which calculates the dates of the workitems based on
1. The owner
2. The availability of the owner, The absences and Allocations
3. The Estimates for the work item.
4. The predecessor or successor links to the work item.
5. The constraint type and constraint date of the work item.
Based on the above the scheduler schedules the work items for different users in the plan.
There will be no case where the user will be scheduled to work on 2 work items.
If you want to changes the dates you can do so by modifying the above attributes.
You can find more info in https://jazz.net/library/article/657