The limiting factors on what cartridge you can barrel an action for are not only the chamber pressure rating, but the diameter of the case itself. The reason for that is that at a given chamber pressure, the total backthrust against the breech is equal to the crossectional area of the cartridge case. Simple physics are involved and you do not want to overstress that model 44 action.
Say your .32-40 cartridge is rated at 30,000 CUP which may translate to XX,000 psi. The same cartrige casehead size "family" would include .30-30, .25-35, and .38-55. You can likely chamber for all three cartridges IF you limit yourself to the original blackpowder chamber pressure equivalents.
However, if you chamber your rifle to say, the .40-65 or .45-60, .45-70 casehead size family and limit your loads to the same 30,000 CUP or XX,000 psi rating, the breechblock backthrust is now some 150% of what it was for the smaller .32-40 casehead size. You can calculate it for yoruself. Measure the base diameter of the cartridge cases and calculate cross-sectional area. The breechthrust for the larger casehead is a LOT more.
According to the late Frank "Mr. Singleshot" De Haas, the Stevens 44 action is a realtively weak one, and rechambering for other cartridges should be done with great caution. You should get a copy of his "Single Shot Rifles and Actions" and read up on it. I don't have the book in front of me at the moment, but as I recall, even the last of the improved model 44 rifles were considered unsuitable for a mild cartridge like the .22 Hornet.
In my opinion, even chambering for one of the .45-70 casehead sized cartridges and loading to blackpowder pressures is taking a considerable risk. The materials and design of the model 44 are not up to the task.
Have fun with your rebarrelling project, but please play it SAFE.