I agree it sounds like you have way too many groups. If you can reduce the number of groups on your dependent variable side, then the analysis you need to predict group membership from continuous predictors is discriminant analysis.
With two samples per actegory you can not do much. So, you will have to build smaller groups as all the other collegues said. To do so, you can apply "business rules" (prior knowledge about the categories) or if you do not have such information you can do some exploratory analysis by means of clustering or PCA. For instance, you can do consensus clustering to try to figure out the number of groups you really have in your data.
Unfortunately, the solution to my problem can´t be summarizing groups I guess. Maybe I can quickly explain the problem:
My samples are mother-pup pairs (1 mum, 1 pup per group). My predictors are scores resulting from a factor analysis on the olfactory profile. Now I want to see whether one of the factors represents the substances accounting for mother-offspring similarity and would thus be significant in a model where mother-offspring group would be the categorical dependent variable.
I think that you could group by means of score similarity trhough some clustering or PCA like method. If groups emerge there, then you can summarize a kind of meta mother-pump class.
I'm not sure how the mother-offspring group is quantified. But if I understand correctly, you have 41 observations of mothers and associated 41 observations of pups, and four IV. You want to see which of the four IV predict the two DV. Put that way, it sounds like multivariate multiple regression with 2 DV and 4 IV.