This is a discussion I've been having with other developers on whether his is allowed on itch or not.

Let's say I want my project to appear in the New section as often as possible. In order to do that, I publish the version 0.1 of my game and offer it up for $5 in purchase or donation. The next month, I hide version 0.1 page, create a new one with version 0.2 of my game and sell it for $5 and publish it, rinse and repeat every month and every content update.

In this scenario, people who purchased older versions can still see and download them, but they'd have to pay me $5 again and again at every update, because these will be considered different products on itch.

Is this allowed on itchio, or would we eventually be asked to stop doing that and keep everything in a single project?

What you suggest is frowned upon. The idea here is that people buy the game once and then updates are free. That's only fair when you start with the game in early access like you describe. How many times should they buy it until it's done?

Consider making a new project page only later, when you make a special edition of the game with lots of exclusive content or fundamental changes.