How to have base salary on employee level as opposed to assignment level for only one group

Summary:

Currently in our organization, all base salary is at assignment level for all groups of employee. Only for one group, we want the base salary to be at employee level and not at assignment level. This group will not have multiple assignments at the same time. But it possible the employee remains in the same group but changes assignment. Is it possible in our current architecture, where the for the rest of the group the salary is on assignment level

Note: The employee assignment status such as active, suspended, LTD is updated on the assignment level. Any help is appreciated. I only have compensation and Benefits module knowledge, not sure if I need to involve HR Core for this change.