I'm not sure I can provide much advice, but here are my thoughts:
Note: Much depends on how you got the data you are trying to model.
1. First, you should check for correlation among your multiple Y's (Analyze>Multivariate Methods>Multivariate). When there is significant positive correlation, the models will be similar. If, the correlation is something else or insignificant, the models for each Y can be quite different.
2. Optimization in a multivariate environment can be quite challenging. It might require using alternative measures (Y's). It might require complete re-design of the process (which can include identification of factors not previously considered and which may not be significant in a univariate approach). And likely it will require some trade-offs.
3. I believe the Group Fit platform in JMP will provide Profilers for each of Y's simultaneously so you can evaluate what happens to each Y as the model is changed for any one Y.
4. Depending on how you get your data there are other options to evaluate the multiple Y's (e.g., overlays of the surfaces)
"All models are wrong, some are useful" G.E.P. Box