AFAIK, there's certainly nothing on the drawing board that would be big enough to actually accommodate human experiments. This seems like one of the highest value things NASA could do with ISS.
Voyager Station is a planned microgravity enviroment which plans to be in orbit at 2027. It will likely be a lot cheaper to do those experiments on voyager station then on the ISS.
You have not really succeeded in colonizing another place unless you can make all the essentials for continued life locally. This in turn has the limiting factor not just on biology, but how machinery wears out, ergo you need a way to manufacture all the critical machinery, and the machinery to make that machinery, and so on.
The solution to this ironically might allow you to bypass the issue entirely. If you have self-replicating industrial plants, why deal with all the hassles of a planet? Why not just export (using mass drivers) from the industrial plants on the surface the components for a decent orbital habitat?
The habitat would basically be one can inside another. In between the 2 cans is sand (mining tailings), 30-100m, enough to bring interior radiation doses to levels seen on earth.
Ribs on the inner can (think the hoops you see on a soup can) host maglev tracks. Riding the tracks are circular trains. Spun fast enough to reach 1 G if necessary. Angular momentum of the entire habitat is kept at zero, this is done by having half the trains drive the opposite way. (and there are transfer trains that let you move from one set to the other).
You can have all the trains stop (in coordination with each other) for maintenance.
Of course the easiest way to avoid the 'kids are fragile' issue is to not need such incredible numbers of them. If your colonists live for centuries and don't just start decaying a mere decade or 2 after you are finished training them, you don't have to have most of your colonists unproductively being in school or old-age care most of the their lives, you only need a tiny percentage of the population to be new children, individual colonists live long enough to actually earn the millions of (inflation adjusted) dollars a colonist seat in our near future will cost, and so on.
It occurs to me that our ancestors with their focus on the possibilities of space travel and colonization might have been missing the real problem...
Worst case, women on Mars will spend their pregnancy in a centrifuge. Someone please use this in a movie!
No, worst case is the entire developmental trajectory of infants and children might also get messed up. If gestation in martian G isn't safe, at what point post delivery is Martian G safe?
Also, on a practical level: can you imagine how unpleasant being stuck in a centrifuge for nine months while pregnant would be?
Did you know that just changing the orientation of chicken and frog eggs while they're gestating can mess things up? Never mind actually changing the magnitude of the g vector.
The lack of basic research in this area is not good. The moon has around 1/3 g. Mars around 2/3g. Can baseline humans and other large mammals reproduce successfully at that acceleration? I'm just an internet know-nothing know-it-all, but I give 70% against lunar G being sufficient and 60% against Martian.
We don't have good ways to study this on earth. We've done fun stuff like fly human jizz on a vomet-comet and roll plants, cells, tissue samples and small animals around in Clinostats and Random Positioning Machines (big, slow-moving rotating drums and gimbaled doohickies). But apparently all we really know is that larger mammals don't have the specific vulnerabilities that birds and frogs do: having a yolk seems to make them more sensitive to the direction of G, because of chemical diffusion:
Gravity sensing in individual cells in mammals has also not yet been defined. Unlike frog, where free-living embryos arise from oocytes with maternally differentially-deposited nutritional heavy yolk, mammalian embryos rely on maternal nutrition after implantation and have little yolk. Thus, mouse embryos are not thought to sense gravity by macromolecular (yolk) distribution sensed by the cytoskeleton, as reported in frog..
AFAICT, there's no large centrifuge on the ISS -- JAXA built a module intended to house a decently sized centrifuge (specimens up to 24" tall), but the plans to launch it were cancelled. AFAIK, there's certainly nothing on the drawing board that would be big enough to actually accommodate human experiments. This seems like one of the highest value things NASA could do with ISS.
My guess is that if 0.38g ain't enough this will probably need some next-level genetic engineering to be worked around.