Potential problems with paralleling a jumbo battery to iphone internal battery?
Don't bother.  Here are the issues:


The circuit you are connecting this to is not going to expect the higher charging current and at best won't know how to behave.  At worst it might damage something.
There is software inside the iPhone that tracks the rate of discharge and estimates the remaining power.  This software will do some learning, to adjust for battery differences, but it is unlikely to adjust for a 2x or 3x capacity increase.


You would be better off making what is essentially a USB battery pack.  A battery that has a USB jack on it so you can plug in various USB devices to charge them.  This would be a cleaner design (no weird wires coming out of your iPhone) and would also work with other devices without modification.