I'm not aware of a hard limit on how often you can modify that pricing. I would of course effort to avoid rapid/back-to-back changes so that the system can keep up, and users aren't peppered with too frequent notifications etc.
Is there some specific scheme you have in mind that prompts the question?
Otherwise, see: https://developer.apple.com/app-store/subscriptions/
There are no limits.
Each time you increase the price of an autorenewable it stops autorenewing and requests a confirmation from the user before the next scheduled renewal. I suspect that multiple price increases between subscription periods will result in multiple requests to the same user.
The price charged for a renewal is by default the then current price not the original price. (But there are ways to change that.)