I don't think we necessarily have to sacrifice something. We learn new skills and knowledge all the time. Using the new limb could be a skill. Maybe it's not as dexterous as the motor cortex and real hands at first, but there might be some benefits over natural hands.
I think that you sacrifice something when you learn a new skill. The brain have a finite capacity and it just forget not used facts or skills, and the reason it's forgetting is because it's always learning.
For instance, I'm learning German and I can feel how is messing with my English, specially with the spelling (English is not my first language).
I think memory retention has more to do with simplicity / emotional consistency.
The new skill you learn may reinforce existing areas if its components are transferrable. Also, I see schemas as compression in the brain; eidetic memory shows how much some brains are capable of.
Forgetting is very good for clarification. I think your example suggests that your spelling in English hasn't been established deeply enough; I understand why you might have an adverse reaction to learning it though (German spelling is far more reasonable).
But if it has a finite capacity, when does it fill completely and with what? I guess it's entirely possible that only kids who are growing up can learn to use the extra limb and adults won't be able to.
I don't think it never fills completely, it just empties the older entries to make place for the new ones.
Because the part that you would use to control your extra tentacle or whatever is probably currently used for something. If you are missing an arm is obvious what part of your brain you would use, otherwise, some sacrifice probably have to happen.
Even reading, it seems, take the space that is used in people that can't read for some detailed visual processing (1).
Maybe you could add some extra processing in the extra arm, so it's more "cheap" to use.
(1) - I learnt that in "Reading in the brain" by Stanislas Dehaene.