Run multiple instance of any windows application
There is no generic way because different applications use different methods. Many of the methods involve trying to get some machine-wide (or, at least, user-wide) resource (e.g., a named synchronization object, a file with a well-known name and location, or a registry value). If the app succeeds, then it holds that resource as long as it runs. If it fails because another instance already holds the resource, then it might try to signal the original instance so that it can respond.
In 16-bit Windows, when a program started, the OS passed it a unique handle called an HINSTANCE. It would also be passed the HINSTANCE of a currently running process using the same executable (if any). In those days, that was probably the most common way for the program to know if a copy was already running. In 32-bit Windows, with protected memory, process-specific address spaces, and the end of cooperative multitasking, the HINSTANCEs no longer carried the same meaning.
A small number of apps do this simply for "usability", but for many others, there may be a good reason to enforce singletons. Bypassing that could lead to data corruption or simply failing to run.
Many applications check the global list of processes (with EnumProcesses, OpenProcess, GetModuleBaseName, and similar functions) or list of windows (with EnumWindows, EnumChildWindows).
You may try to set hook (see samples SetWindowsHookEx, CallNextHookEx, etc) to hook those specific API function calls from that application and replace requested data in response with yours to fool the application.
You can run application on different users accounts and instance checking will not work anymore.