Why would you over expose and underdevelop on a rainy and cloudy day, with presumably flat lighting? To me that would be counter productive.
I've stopped pushing my film on gloomy days and instead, started pulling it. I think that attempting to restore flat local contrast by increasing negative contrast through exposure and processing is a sucker's game because local contrast still won't be right but, the highlights and shadows won't fit on the paper either. In other words, if you could possibly increase the negative contrast enough to restore local contrast, its overall density range would be absurd. It seems to me that the only decent way to restore proper local contrast is on the paper. And doing so often spills the shadows and highlights off the paper. So counter-intuitively, I pull my film when it's gloomy out, knowing that I will be grabbing a #4 filter. Using the high paper grade restores a normal, crisp local contrast and the contracted negative will require minimal D&B.