It is not possible to hide a message, without modifying the wet pixels, if there are too many wet pixels. Think for example, of an image with all pixels wet: you can't modify the image without modifying some wet pixel.
The only options in these cases are to modify the wet pixels or hide less information.
Other more advanced options, such as STC, allow you to indicate a cost for each pixel. Therefore, the modification of the pixels with the lowest cost will be prioritized. In this case, the equivalent of the wet pixel is the pixel with infinite cost. But even in this case, these pixels can end up being changed if there are too many of them or if the message is too big.
You can learn more about this in the following paper, in which the amount of modified wet pixels is studied.
Minimizing Additive Distortion in Steganography Using Syndrome-Trellis
Codes by T. Filler, J. Judas and J. Fridrich. [ PDF ].