The next step is a Gamma stage, if they want to be formal about a next round of testing. What most places tend to do, however, is just release the next test build as a "beta build 2" or some other increment tacked to a "beta". But formally it's considered a gamma stage.. unless they have some serious issues and have many more testing cycles to do. In that case, it's a perpetual beta until it's release. Alpha is like.. the absolute lowest testing you do right when the developers finish, and it's usually a closed testing group.

The only time a beta returns to an alpha is when there's some really serious issues. It's almost like saying the beta release was a mistake.

Now there are things like multiple beta releases, and multiple alpha releases. Usually called builds. Alpha build 1.0.1, Alpha build 1.0.2, etc.

I'm about to enter an alpha stange on the program I'm working on this week. Wish me well. 6 months development about to come to a close.