Partially lift with liftIO

I'm trying to do something that's probably impossible. I have a type that is an instance of MonadIO . If you liftIO an IO action in a context where this type is the base monad of some transformer stack, it will work fine. So, what I'd like to be able to do is take a value that's already been lifted part-way (to my type) and lift it "the rest of the way" in one step.

I can do this in two ways. One is that my type can actually be trivially re-embedded into normal IO, so I can do this:

liftMore :: (MonadIO m) => MyType a -> m a
liftMore x = liftIO $ embedMyTypeInIO x

And this works. However, this also provides a way to fully escape from my type if used in context where just IO is the base monad, which is undesirable.

I can also do this by building a new typeclass like MonadIO that uses my type as a base, but then it needs to be instantiated for everything, which is very undesirable. I tried using a newtype wrapper to make every monad transformer an instance of such a class, but couldn't quite get it.

Any ideas on strategies I could try to accomplish this? (I'm willing to play with language extensions, but of course a solution that is Haskell98 is much preferrable).

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