If stage server differs from production - you won't be able to extrapolate the results and calculate the anticipated metrics based on results from the different server.
In this case you can utilize your existing test results from integration or soak testing perspective as the bottleneck might be connected with a 3rd-party component like database which can be tested separately using JDBC Test Elements
But you cannot state that i.e. if stage server has A
GB of RAM and you were able to reach B
requests per second then prod server which has A*2
GB of RAM will give you B*2
requests per second.