Were you requested to create a new AppServer that was identical to the one you already have? Or a new AppServer that was configured slightly differently?
Unity and Web Client may require different authentication or may require the AppServer to be configured differently in some other way than the custom applications that connect using Unity API.
CreateDomainAuthenticationProperties() indicates using Windows authentication at the AppServer level when connecting via Unity API. You may need to check what settings were needed for your Unity and Web Client to work on the AppServer level.
As others have mentioned multiple AppServers can be run on the same Windows server you shouldn't need a change to your number of servers or architecture.
Having said that, embracing separate AppServers are for different clients is actually a good thing so that they can use different AppPools so that:
1) recycling one AppPool wouldn't affect everything else.
2) a crash in one of the AppPools wouldn't affect everything else.
3) they can have be run under different credentials there is any such need.
4) they can have different configurations such as timeout settings, # of worker processes, memory limits, fail protection settings etc.
The only downside to running different AppServers (within the same Windows server) is there is slightly more memory used since each AppPool has some memory overhead. This is usually only a few hundred MBs but is considered negligible since servers usually have memory in the GB ranges assigned to them.
