# Can odds ratios increase if you include more variables?

Suppose one wants to compute the odds ratio of a disease for a person in group $A$ versus that of a person in group $B$. Suppose we consider the following: (i) include age in the odds ratio calculation, (ii) include age and height in the odds ratio calculation. Is it possible for the odds ratio for (ii) to be much greater than the odds ratio of (i)?

If you are to look at the calculation (taken from wikipedia on logistic regression), the model is $1/(1+e^{-z})$; so as $z$ gets larger, the odds would increase as well.