As noted a few times, the Alt-1915 league I'm running differs from reality by adding two teams to both the American (Kansas City and Newark) and National (Buffalo and Baltimore) Leagues. As a result of the backstory that gets us there, the court case that confirmed MLB's anti-trust exemption never happens. Also, instead of the Federal League ending pretty ignominiously, it can be seen as a partial victory since half of the teams survived.
So, what does all this imply? Obviously, details will depend on the records of various teams and I'm not making specific decisions yet, but...
There are still the conditions in place for future challenges to MLB: There are still underserved parts of the country, and I think the reserve clause is still in place. On top of that, four fewer high-level minor league cities exist (so there will be fewer high-quality minor leagues?). Milwaukee will be by far the largest city, and the only one in the 16 largest US cities (by 1920 population) without an MLB team. However, there are a few other cities that seem like plausible sites for MLB teams based on 1920 population and 1930 population: Minneapolis was larger than Kansas City in 1920, and maintained that advantage through 1930. The same was true of New Orleans, Los Angeles, and San Francisco. Indianapolis and Seattle were smaller than Kansas City, but larger in 1930 than Kansas City had been in 1920.
Early expansion might be possible: Given that, and given the 10-15 year timeframe on which challenges to MLB had been happening, it seems like the mid-late 1920s would be when the next wave would occur. Maybe it would be another threatened league, maybe would-be team owners approach MLB and ask to buy in and replicate the Federal League results without going through the middle parts. Without an anti-trust exemption in place, maybe MLB is proactive rather than waiting for what they consider an inevitable challenge. The NL had been a 12-team league for most of the 1890s, so expansion to 12-team leagues might not be outlandish (though whether they'd split into divisions or not isn't clear to me).
Where might they put teams? Milwaukee is the obvious spot. Minneapolis would be an obvious 2nd team. Would they expand just one league? Maybe. If two other teams were needed, where could they go? New Orleans seems tempting, but it also seems a bit far. The West Coast is definitely too far in the mid-20s. There are two other very large cities that I haven't mentioned so far, though--Montreal and Toronto. Both had 500,000+ inhabitants in 1920, which would make them the largest cities in North America without MLB. They grew even larger by 1930 (though LA would grow even faster and pass them). The International League existed in real life from 1915 or so onward, and had teams in both cities, giving the existence proof that the border wouldn't cause problems. They weren't terribly far from existing teams, but far enough to be distinct cities. They were on existing transportation networks. Given all this, a mid/late-20s expansion to Milwaukee/Minneapolis/Toronto/Montreal seems reasonable.
Only one early relocation seems likely: I mentioned Harry Sinclair's future legal problems elsewhere. These would probably slightly predate (or maybe come at the same time?) as the possible early expansion. If Newark was coming off of a decade of terrible teams with poor attendance and was hemorrhaging money, a new owner might be eager to move out of Newark. Again, Milwaukee would be the obvious place to go, but given what I was just saying I might be talking myself into Toronto as the place to move. In any case, if there was a move, it'd require coming up with one more expansion site. And if Newark is doing really well, I don't see why they'd move. I don't see other moves as terribly likely before 1940, for the reasons I gave in previous posts--it took that long for the effects of radio to make clear that some cities could only really support one team and I don't see any obvious reasons for teams to bail out of their home cities before then.
Timing of general relocations could be a bit earlier than in real life, but probably not that much: As I noted, I don't see teams moving before 1940. I have no idea how the game will deal with the Depression or WWII, but if they have an effect I'll try to adapt as the real teams did. And, again, if 1940 or 1950 or 1960 (assuming I get that far) finds both the Browns and Cardinals (for instance) in great shape, I don't see why they couldn't both stay in St. Louis. Once the relocations do seem like they'd happen, though, I think they could go anywhere in North America that makes sense--the Browns' would-be move in 1942 shows that LA would have been doable then. People argue that it wouldn't make sense for just one team to move, but the Browns attempted move suggests otherwise. Still, even without any late 20's expansion or a move by the Peppers, there's not too many other places for teams to go other than the West Coast and there will almost certainly be 3-7 teams looking to move. The details might also differ, as I've probably beaten into the ground by now--the Dodgers and Giants shared New York for 60-70 years, and there was nothing inevitable about the most intense part of their rivalry occurring just as they were looking to move. So, maybe one moves but not the other, just like things were heading if Robert Moses gave the Dodgers a domed stadium in Brooklyn. Maybe it's the Cubs and the Cardinals that move together. Heck, maybe the Peppers and Athletics will have some intense multi-decade rivalry and also be the ones who have to move out of their cities.
I have no idea how a second wave of expansion/relocations will go, but that's part of the fun: So, I guess I'm outlining a scenario that gives MLB 24 teams by 1930, which is about 40 years before they had that many in real life. Alt-1915 will likely have teams in Buffalo and Toronto at its 24-team stage, which real-life MLB24 didn't, but MLB24 had teams in San Diego, Atlanta, and (eventually) Dallas, which I don't see Alt-1915 having in 1930 or even 1950. It's possible that early expansion will indicate a mindset that will lead to a much larger MLB than we have now--40 teams by 2000? Maybe the weakened minors in the East (especially if an early expansion takes up even more of the main cities of the real-life International League and American Association) would lead to a push for the Pacific Coast League to be a major league? When we think that a city is too small to host a major league team, that's based on a particular history and economic model that may not have been inevitable had different choices been made earlier. It's not terribly hard for me to imagine MLB teams in most of the places with NFL/NBA/NHL* teams that lack MLB: Memphis, Jacksonville, Nashville, Charlotte, Vancouver, Sacramento, New Orleans, Vegas, Columbus, Portland... Heck, Salt Lake City has had an NBA team for over 40 years.
OK, I think it's time to close this post. In the last day or two I've been thinking about that second wave a bit more. Maybe I'll post more thoughts soon, even though it will likely be a few real-time years before they matter!
*The NHL also has a bunch of cities that clearly won't work, I think? Like, all the ones where it's going to be frigid at the start of the season. Maybe you could put domes in Calgary or Edmonton or something in the 70s, but I don't know if they win out?