As with any change attempt, the first thing is to identify who the supporters are and who are against it. It’s important to understand the reasons some employees have for supporting the new type of review system as well the reasons of those who do not. Small-group sessions where workers feel safe to express themselves would help to elicit honest communication of the fears and concerns of those with varying perspectives.
Before creating a new 360-degree review system that is cast in stone, give employees a second opportunity to communicate their concerns over a specific new model program, this time allowing for the airing of possible changes and modifications which may address still outstanding issues.
Finally, I would explain that any program or policy is always evolving to meet the changing needs of employees and the organization. As such, this new 360-degree review can be presented as one which is open to modification and adaptation over time as deemed appropriate by all involved.