public interface IInterface1 {};
public interface IEtcetera {};

public struct CanUseThis : IEtcetera, IInterface1 {}
public class  OrThat     : IEtcetera, IInterface1 {}

public class Foo
{
    private IInterface1 _object; // just pick one

    public void setObject<T>(T obj)
        where T : IInterface1, IEtcetera
    {
        // you now *know* that object supports all the interfaces
        // you don't need the compiler to remind you
        _object = obj; 
    }

    public void ExerciseObject()
    { 
        // completely safe due to the constraints on setObject<T>
        IEtcetera itf = (IEtcetera) _object;

        // ....
    }
}

public class Program
{
    public static void Main(string[] args)
    {
        var foo = new Foo();

        foo.setObject(new CanUseThis());
        foo.ExerciseObject();

        foo.setObject(new OrThat());
        foo.ExerciseObject();
    }
}