To present a convincing argument to the nursing manager, you should be able to clearly and concisely explain the reasons why additional RNs are needed due to the patient variables not being accounted for in your database. To begin, I would gather data from staff about factors that contribute to a higher workload than normal such as an increased patient complexity and acuity level. Then present the information organized. It will support my argument and also show how the database may not reflect these variables accurately.
If budget permits, I might suggest hiring temporary staff or using agency nurses to fill any gaps until permanent personnel can be arranged. This way both immediate short-term needs and future long-term challenges are addressed in order to ensure the best outcome possible no matter what challenge they face at a given moment. Also, if the budget is there, you might consider hiring agency nurses to cover any shortfalls until permanent staff can be hired.
Finding common ground is the most important goal since, ultimately, everyone wants a successful solution to whatever problem may be presented.