New amp models are such a secret, and part of the fun. Sometimes you'll find Cliff will drop hints or just let you know what's coming down the pike. Just follow his posts, and if the mood strikes him, he'll let us know something. E.g., he posted about the Griddle Cake drive when he ordered it. I think it's fine to pine after particular amps that are not in the Axe, but from what I've gleaned as a total layman, many amps are really just minor tweaks of existing famous circuits. So if there is any particular amp you're interested in, it's always great just to create a thread and ask forum members what it would take to approximate it in the Axe. There are quite a few members here who really know a ton about amp design, and they're really cool and generous with their advice about how to achieve different emulations.
And of course, just choosing an amp that's close in your mind to what you like, and starting to do your own mods is a fun as hell rabbit hole. For true tone hounds, I would think nothing could be better, since you can tailor the response of any amp model to your guitar, your playing style, your favorite IRs, etc. I just think it's the bees kness.
And finally, I think it's really really really really worth it to take a look at the wiki list of amp models and check out Cliff's creations. I say it's good to use the wiki because not all his creations start with FAS in the title. So if you'd like, e.g., to try a version of an amp that is idealized according to Cliff, you've got a suite of one's to choose from. The response of these amps is really something; it's just so easy to dial in exactly what he was intending with those.
I also used to follow Cliff's posts on The Gear Page forum to see if I could learn anything about upcoming features, or just how better to use the tools already available in the Axe.
Owning an Axe-FX III is like joining a tone club, where you get gifts all the time just for being a member. To echo the most true cliché, what a time to be a guitarist.
