Well it depends on the details, of course. Nonlinear warping is often done for distortion correction. So things like blip-up/blip-down distortion and B0 field map correction require computing a nonlinear warp to apply to the EPI data. A single nonlinear warp is applied to all the EPI volumes equally for the purpose. Often this is combined with affine transformation for motion correction and for alignment to a corresponding anatomical dataset. Additionally, affine and nonlinear warps are concatenated and applied to bring the processsed data into a standard template space.

Usually we compute an affine alignment between the EPI data and the anatomical data. Is the result not good at that step of the alignment? Or are you not seeing good alignment of the anatomical dataset to a template? There we do use a nonlinear warp to align the data to the template. You can potentially increase the weighting for some areas or allow for more distortion. Or do separate analyses with different alignments. The cerebellum is a bit trickier thant other areas because it hangs very differently from one person to another. That sometimes makes a separate cerebellum analysis necessary. Jorn Diedrichsen made a separate cerebellum template and atlas for this purpose.

We generally do not apply a different nonlinear warp for the purpose of motion correction though. For this to work at all, you need to have exceptionally good structural resolution. I've tried something similar in the past, and I've seen best performance visually with an inilev and maxlev both set to 4, so no big warps and no tiny warps. That was for that particular data, and your data will be different. In the end, we decided against it, because there is still some arbitrary warping inside areas that have little visible structure in the EPI data.