When we want to add a problem from one contest to another, there is an option attach to another contest. However, it is quite inconvenient to use when we have multiple problems to add. I'd suggest having a checkbox next to each problem in the contest admin's view and an option to add all the checked problems to another contest in bulk. With this, we could add more actions that we can perform for multiple problems at the same time i.e. assigning many problems to a single round.
The concept design can be seen here