What you are describing would be "easily" accomplished in native COM by creating an out-of-process COM server (also commonly referred to as an ActiveX EXE). As the name implies, an out-of-process COM server runs in its own process and serves it's methods via a COM interface. If multiple clients use the COM server simultaneously, they both share the same server process, so any global data within that process is shared between all of the clients.
Unfortunately, .NET does not provide any mechanism for creating an out-of-process COM server. All COM visible .NET assemblies act as in-process COM libraries, so each client using it has it's own set of global data within their own processes.
The only alternative is to create a standard in-process COM-visible library, but have it just be a pass-through wrapper which calls out to some other process. Inter-process communication in .NET is typically handled with WCF, so the typical solution would be to have a WCF service running in the back-end with which the COM-visible library communicates. If you don't want to use WCF, you could also look at .NET Remoting or raw TCP/IP sockets.
Here's a chicken-scratch diagram to help visualize what I mean:
