Yes, the standard viewing situation which the DOF calculation applies to, is an 8x10 inch print, viewed at 10 inches. Circle of Confusion (CoC, see Wikipedia) is an arbitrary factor in that calculation (about how well the eye sees the magnified blurriness in the enlargement).
If you print it 3 or 4 times that 8x10 size, then the allowable Circle of Confusion becomes 1/3 or 1/4 size too, because it will be enlarged 3 or 4 times. CoC is not a "hard fact", it is just someones considered judgement about what the eye can see at the 8x10 inch degree of enlargement. CoC has become smaller today, due to better film, and better digital. But enlarged CoC is key for the DOF calculation.
So as far as calculating DOF, then in the DOF calculator (in the 3x or 4x case), you could choose another camera (smaller sensor size) that gives a CoC 1/3 or 1/4 the original CoC size given for your camera. Camera model does not matter, it is about sensor size, specifically only about its necessary enlargement to 8x10 size. 1/3 CoC size, enlarged 3x more, gives the same numbers.
However... a big deal - viewing distance of large prints is yet another factor of DOF (for the eye). Unless you still view it at the standard 10 inches (held close under your nose), then 3 or 4 times viewing distance increases the allowable CoC that much, the opposite effect, which in actuality, probably cancels out the enlargement factor. Like billboards, large prints do look good when viewed from across the room.