Is there a Gaussian Mixture Model for data with opposing pairs?

I have a classification problem with data that comes in pairs. A pair consists of two datapoints (A,B) or (B,A), each datapoint containing 20 features.

After receiving about 30 pairs, my goal is to separate the A and B classes using a GMM using feature similarity. For each datapoint, it is not known beforehand to what class it belongs, but it is however known that is of the opposite class as the other datapoint in its pair.

Is there any existing GMM method that has the possibility to include such information using restrictions or an extra feature?

One possible method I can think of would be to include one extra variable to the GMM per pair. This would be valued 0 for the first datapoint of a pair, 1 for the second datapoint and 0.5 for all other points in other pairs. A problem of this is that it would require an additional 30 dimensions on the GMM and the effectiveness is unclear.

Can someone help me with this problem?