Ensemble models - neural network input both original data and predictions of other models?
I suggest you test it by cross-validation to prevent overfitting. However, I guess because of a strong relationship between this variable and output your work will not be better. Instead, try to use an ensemble.

I read something about deep learning which in that way they use several models as a sequence and use results of previous models as inputs of the next models. Maybe if you continue this work it will be in some way a deep learning.