There is way more variation than I expected to find. I've got treadle machines made by
Davis
Wheeler Wilson
Singer
White
National
New Home
Standard
Household
Domestic (pre White)
Free
Eldredge (pre National)
Foley & Wilson
all of them will work with the cast iron base - as long as you get the machine lined up so the belt grove on the flywheel of the machine lines up with the flywheel below. keep in mind, some machines run counter clockwise and some clockwise - but it does not matter once you get the wheel spinning, you just have to start it in the other direction.
if you don't wish to modify the cabinet -
Differences include:
Size of base of machine (opening in cabinet) This also includes any flip up opening needed to drop the machine. You have to make sure the machine will clear when. I've put non-Singers in Singer cabinets only to find I could not lower them as the flywheel hit a metal support bracket - but that's not too hard to move - these were electric machines though.
Depth and diameter of hinge pin (and even type of hinge, not all are pins)
Location of belt grove in flywheel in relation to base of machine
Method to secure machine to cabinet (so it won't fall out when cabinet is closed).
If you are interested in later made models, there are less variations - and after a while, they got quite standardized.