Well, here's one way of doing it. You have lots of choices here; these are the decisions I made in implementing the code:

* myFuncB no longer lives in the IO monad. I wasn't sure if you specifically wanted that, but now it can work with *any* instance of Failure.
* Since I assumed you ultimately wanted it to land in the IO monad, I defined Exception instances. However, if you were dealing with a different Failure instance (like [] or Maybe), these would be unncesary.
* I also assume that what you meant by "your code" and "their code" is that you can modify your own code, but not theirs.

If you show me what the real code is you're working on, I'd be happy to more fully develop a better solution with you. Anyway, here's the code.

Michael

{-# LANGUAGE FlexibleContexts #-}
{-# LANGUAGE DeriveDataTypeable #-}
{-# LANGUAGE StandaloneDeriving #-}
import Control.Failure
import Data.Typeable (Typeable)
import Control.Exception (Exception)

-- Theirs (other library code stubs)
data TheirError = TheirErrorCase deriving Show
data TheirData  = TheirData deriving Show

theirFunc :: [String] -> Either TheirError TheirData
theirFunc = undefined


-- Mine (my own code stubs)
data MyError = MyErrorCase deriving (Show, Typeable)
instance Exception MyError
deriving instance Typeable TheirError
instance Exception TheirError
data MyData  = MyData deriving Show

myFuncA :: MonadFailure MyError m => TheirData -> m MyData
--myFuncA :: TheirData -> Either MyError MyData
myFuncA = undefined


myFuncB :: (MonadFailure MyError m, MonadFailure TheirError m)
        => m MyData
myFuncB = do
   x <- try $ theirFunc []
   myFuncA x