Всем спасибо, пока сделал так

using System;

namespace ConsoleApp17
{
    class Program
    {
        static void Main(string[] args)
        {
            Class @object = new Class();
            IBase @base = @object;
            IDerived1 derived1 = @object;
            IDerived2 derived2 = @object;

            @base.Do();
            derived1.Do();
            derived2.Do();

            Do<IBase>(@base);
            Do<IDerived1>(derived1);
            Do<IDerived2>(derived2);

            Console.ReadLine();
        }

        public static void Do<TClass>(TClass @object) 
            where TClass : IBase

        {
            if (typeof(TClass) == typeof(IDerived1))
                ((IDerived1) @object).Do();
            else if (typeof(TClass) == typeof(IDerived2))
                ((IDerived2) @object).Do();
            else
                ((IBase) @object).Do();
        }

    }

    public class Class : IDerived1, IDerived2
    {
        #region Implementation of IBase

        void IBase.Do()
        {
            Console.WriteLine("IBase");
        }

        void IDerived1.Do()
        {
            Console.WriteLine("IDerived1");
        }

        void IDerived2.Do()
        {
            Console.WriteLine("IDerived2");
        }
        #endregion
    }

    public interface IBase
    {
        void Do();
    }

    public interface IDerived1 : IBase
    {
        new void Do();
    }

    public interface IDerived2 : IBase
    {
        new void Do();
    }

}

Всем спасибо, c рефлешеном, понятно, что можно всё, но производительность страдает,
пока сделал так

using System;

namespace ConsoleApp17
{
    class Program
    {
        static void Main(string[] args)
        {
            Class @object = new Class();
            IBase @base = @object;
            IDerived1 derived1 = @object;
            IDerived2 derived2 = @object;

            @base.Do();
            derived1.Do();
            derived2.Do();

            Do<IBase>(@base);
            Do<IDerived1>(derived1);
            Do<IDerived2>(derived2);

            Console.ReadLine();
        }

        public static void Do<TClass>(TClass @object) 
            where TClass : IBase

        {
            if (typeof(TClass) == typeof(IDerived1))
                ((IDerived1) @object).Do();
            else if (typeof(TClass) == typeof(IDerived2))
                ((IDerived2) @object).Do();
            else
                ((IBase) @object).Do();
        }

    }

    public class Class : IDerived1, IDerived2
    {
        #region Implementation of IBase

        void IBase.Do()
        {
            Console.WriteLine("IBase");
        }

        void IDerived1.Do()
        {
            Console.WriteLine("IDerived1");
        }

        void IDerived2.Do()
        {
            Console.WriteLine("IDerived2");
        }
        #endregion
    }

    public interface IBase
    {
        void Do();
    }

    public interface IDerived1 : IBase
    {
        new void Do();
    }

    public interface IDerived2 : IBase
    {
        new void Do();
    }

}