IF such a simple conversion were possible, don't you think that it would already be available as a customisation? Perhaps even as an alternate model direct from the flash unit maker - in the "Ours is bigger than yours" vein? As it's not available, there's likely to be a really, really good reason.
You start off with the premise that
The capacitor usually holds enough charge for 3-4 shots at full power.
It doesn't - as Wilt says, it only holds sufficient for ONE shot at full power with just a tiny reserve to accomodate manufacturing tolerances (usually ±5%, occasionally ±2% on rated capacity with the tighter tolerances really hiking component prices in some cases). Can't even start to imagine where you got the idea that it holds more power; that would imply that makers build redundancy into their units.
So - nice idea but it wouldn't work. If you simply want to increase the number of flashes then just use an external power pack. Easier, cheaper, doesn't invalidate warranty, doesn't fry circuits, doesn't blow the tube (and, oh boy, but those things are expensive to replace because of labour costs).