It's possible with dual licensing. RavenDB (and others) have a similar model where their main OSS project is AGPL, but dev does not require a license, and commercial customers pay for a commercial license. Also, OSS projects can get an exception to allow their OSS license to not be potentially swallowed up by the AGPL. MongoDB instead publishes client libraries as Apache-licensed in order to provide built-in mitigation of the AGPL licensing on its core.
This answer explains pretty well I think. Also do read the comments where someone points out that using it with other licenses is murky water. I had the experience working in a large company that I was blocked from using software on the advice of lawyers because it was GPL.
Personally, I think anyone that decides to release software under AGPL should be slapped with a large trout. It is the most commercially abused license I have seen. AGPL by itself is all but unusable (even for OSS) for the downstream restrictions and legal uncertainties. The software I have run across with AGPL only uses the license to force commercial users to buy a commercial license. This has the potential to setup a situation where the controlling entity uses the OSS community for free labor with one hand while grabbing the financial rewards of the work with the other. The AGPL also effectively prevents forking because only the author can decide to release it under a different (usable) license. It's funny because I believe Affero made the license as a weapon to enforce free software staying free, but the thing about a weapon is, it can be used on anyone.
Before the AGPL the classic way to do what I described above is just to release under an actually-free license to drive contributions and popularity. Once it gets popular, change to commercial at some version. The backlash from this is probably why AGPL method has become more popular, because the one-sided-ness of the arrangement exists from the start but in a more subtle form.