well if the mutually exclusive terms are on the same axis/dimension of the opposites, then: yes.
How do we determine whether two things are on the same axis? Does this imply only one fundamental difference between the two things?
Suppose we have concepts represented by qualitative sets of properties A, B and X, as well as properties a and b.
A = X + a
B = X + b
If there is no concept C in the form X + c where c != pa + qb for some (positive/zero) p and q, and a != b, then A and B are antonyms (with respect to X).
If we instead used three concepts A, B and C, and suppose that no respective concept D exists, then we have an antonymic triplet.
e.g. if we assume that all colours can be formed by mixing the three primary colours, let's say red, blue and yellow.
We have (e.g. R means red, C means is a colour, r is the property of redness):
R = C + r
B = C + b
Y = C + y
X = C + kr + lb + my for an arbitrary colour X and (positive/zero) numbers k, l, m
To determine whether R, B and Y form an antonymic triplet, with respect to C, given our assumption, we suppose that there is some colour Z where
Z != C + kr + lb + my for (positive/zero) numbers k, l and m.
But by our assumptions, all colours can be represented in this way, so they must form an antonymic triplet.
Generalising: if we have a countable set such that any object which contains the properties of the intersection of this set, then if this is an antonymic set, the complement properties of this additional object must be a linear combination of the properties of elements of the set.