If you are looking for the commonly accepted nonparametric regressions like kernel regression and quantile regression, then Fit Model does not support it. However, JMP has a SAS Add-In that may help you. In JMP, select File>SAS>SAS Add-Ins. Of interest to you might be the Loess Regression, Quantile Regression, and Thin Plate Spline procedures. These are good when you don't know a suitable parametric form of the response. Click on the Add-In Help link for details. To use these, you need SAS.
Fit Y by X has a Fit Spline feature, but is only used for a single X. For multiple X's, you can use the Knotted Spline Effect attribute in Fit Model. See the documentation for details on both of these.
The Neural and Gaussian Process platforms are also useful for fitting very flexible regressions models.
