Mock same interface as 2 different types

I have an interface IMyInterface that I am mocking in a unit test using moq.

Mock<IMyInterface> firstMockedObject = new Mock<IMyInterface>();
Mock<IMyInterface> secondMockedObject = new Mock<IMyInterface>();

The unit under test has a register method that looks like this:

public void RegisterHandler(Type type, IHandler handler)

and then a handle method:

public void Handle(IMyInterface objectToHandle)

What I am trying to test is that I can regiester 2 handlers for 2 different implementations of IMyInterface and that the Handle method correctly selects which one to use:

UnitUnderTest.RegisterHAndler(firstMockedObject.Object.GetType(), handler1);
UnitUnderTest.RegisterHAndler(seconMockedObject.Object.GetType(), handler2);

The problem is both mocked objects are of the same type. Is there some way to force Moq to generate 2 mocks of the same interface as different types?