How to train model to predict 1 value from multiple input samples
Is there really any benefit than just creating three different models, and combining them at the end? If the end use case is just to predict the best final models, then I would just train on them individually. 

You could have also do a NN with 3 output nodes, for each target. If you're just looking to do regression or something, I don't see why you wouldn't just predict them independently. There is some literature on multi-output regression (good summary here), but these involve scales of predicting high dimensional vectors(or even matrices), rather than just 3 numbers, so I don't know how useful this literature would be for your case, but that's where I would look if you're insistent on having a single model predict 3 outputs.