trusted RFC from two identical system IDs to same target system

Hi,

we have an active trusted RFC connection from MiddleWare to BackEnd system.

Now we want to establish an other trusted RFC connection from a second MiddleWare system to the same BackEnd. Problem is, that both MW-systems have the same system ID. When trying to establish the trusting in BE-system, we get an error: trusted system entry for system >SysID< already exists.

Is it even possible that one BE-systems trusts two MW-systems with indentical system IDs?

Regards

Stefan