Q:

more than one instance of singleton c#

Is there a realisation of a Singleton-like pattern which allows to create more than one instance?
My class definition is:
public class Logger
{
    private Logger(string logPath)
    {
        this.logPath = logPath;
    }

    /// <summary>
    /// Creates singleton 
    /// </summary>
    /// <param name="logPath"></param>
    /// <returns></returns>
    public static Logger GetInstance(string logPath)
    {
        lock (instanceLock)
        {
            if (logger == null)
            {
                logger = new Logger(logPath);
            }
        }
        return logger;
    }

    public static Logger Instance()
    {
        return logger;
    }

    /// <summary>
    /// Destructor
    /// </summary>
    ~Logger()
    {
        try
        {
            this.Close();
        }
        catch (Exception)
        {
        }
    }
}

A:

Is there a realisation of a Singleton-like pattern which allows to create more than one instance.

If you want multiple instances, just allow the class to be constructed directly, and don't make it a singleton.  In your case, just make the constructor public, and remove the singleton/instance logic.
That being said, there is the Multiton pattern, which allows keyed access to multiple instances via a single interface.

A:

This is the pattern I use:
public class Logger
{
    private Logger(...) { ... }

    static Logger { /* initialize Errors, Warnings */ }

    public static Logger Errors { get; private set; }
    public static Logger Warnings { get; private set; }

    public void Write(string message) { ... }
}

If you want to have a static Logger Lookup(string name) method, you can do that too.
Now in other code you can write Logger.Errors.Write("Some error"); or Logger.Warnings.Write("Some warning");.
Bonus: you can use Environment.StackTrace inside of your Write method to additionally log what method you called Write from.

