Yes Edward, and the Buddhists and the Atheists and etc. will all have their take on it too, but it wasn't the veracity of the addition that I was pointing out. Setting aside the "holy ghost", of whom I deny ;-), it was the properties of duality contained within the Trinity which offered a very unique construct.
ie According to Catholic doctrine, "The Heavenly Father" = God = Jesus = He
So you actually can substitute "Jesus" for "He" in the meaning of the question because of this equivalency, and substitute "The Heavenly Father" for "God" and take it to read:
Q1. Can "The Heavenly Father" create a rock so heavy that Jesus can't lift? Answer 1: Yes, Paradox? No
You can also plug in the values and read the question as:
Q2. Can Jesus create a rock so heavy that "The Heavenly Father" can't lift? Answer 2: No, Paradox? No
In these first 2 cases the paradox is resolved as each form of the question is no longer self-contradictory, even though they contradict each other on the whole.
Further more, the idea of the Trinity also allows for 2 more versions that is inconsistent to the premise of an all mighty being.
Q3. Can "The Heavenly Father" create a rock so heavy that "The Heavenly Father" can't lift? Answer 3: ?!?, Paradox? Yes, if He exists and is omnipotent.
(Which is the standard meaning of the original question)
Q4. Can Jesus create a rock so heavy that Jesus can't lift? Answer 4: ?!?, Paradox? Yes, if He exists and is omnipotent.
In summary, because of the peculiar nature of the Trinity, Catholics are the only ones that have the choice to logically resolve the paradox and answer "yes" to the question, and remain consistent and true to their beliefs. In this case they can prove the plausibility of omnipotence, as long as they excuse themselves and hurry home after they have answered the first form of the question.