Would it make sense to have an output layer connected to other output layers in a NN?

I'm working with data that has multiple variables which could be predicted, nonetheless I need to predict just one that is directly correlated to all of the others. Would it make sense to have a NN that predicts the others first, creating a bunch of output layers connected to the hidden layers, and then have the desired output connected to them? Or it would be better to just have all of the outputs on the same 'level'?