Kodak had a film called pro 1000 (PMZ). I have had success pulling it 2 or more stops on exposure and processing it with a 2 stop pull. The negs had huge grain, were very flat and desaturated. The film started life out with a large grain, vary neutral, narrow pallette, and low contrast.
I have been intending for the past few years to do a series of photo's using this technique with this film, but kodak discontinued the film. A few years, I guess, turned into many.
It may work with newer fast films. The problem is that pulling doesn't always desaturate and newer fast films don't have the big beautiful grain of pro 1000. It might be worth a try though -- or at least I will be trying it.
Bjorke has good advice about investigating techniques used in the pre PS days.
As a rule if you push film (underexpose it and over develope it) you will gain contrast and if you pull film (overexpose it and underdevelop it) you lose contrast.
Saturation is a bit trickier. Pushed film can have a good deal of saturation in the upper end (highlights and brighter mid tones) and not a lot in the mid and lower areas (midtones and shadows). Pulled film can become pretty saturated across the tonal range, especially if the film starts out being a fairly juicy film. Both techniques can enhance grain with pulling doing the better job of it (pushing produces grain mostly in the mids to shadows).
I generally don't shoot fast films so I am not too knowledgeable about which to use. As I recall, it used to be that NPH was very neutral (read dull to my eyes), NPZ had a good deal of punch and that the portra 800 was a neutral film. All these films (or at least the portra and NPH) have been updated since I've last used them.
Playing with the amount of overexposure and under development is how i would try to achieve what you are after. I would start with a neutral film and vary the combinations. You really can't pull process beyond 2 stops, but you can overexpose 1,2,3 or 4 stops and under develope 1 and 2 stops and see what you get.
If you shoot 35mm the grain may not be an issue. You could plan on higher magnification when making prints.
Sorry for the long winded reply.