In Bitcoin script the additional stack doesn't increase its computational power at all: Ignoring the operation count limits, any script using the altstack can be converted with the addition of some extra stack manipulation operations to one that doesn't use it at all.
The claim you're making regarding "two stacks" is technobabble initially created by Wright which was clearly discredited many years ago, e.g.
https://www.reddit.com/r/btc/comments/6hjxiy/new_craig_wrigh...
In Bitcoin script the additional stack doesn't increase its computational power at all: Ignoring the operation count limits, any script using the altstack can be converted with the addition of some extra stack manipulation operations to one that doesn't use it at all.