Are you pushing for stylistic purposes (grain, contrast) or to overcome low-light situations?
Tri-X can be pushed a single stop without changing development times or at the most boosting times by 15%. I’ve done this with Microdol-X and Xtol, both work well but have different characteristics. The Microdol-X developed negatives had the finest grain, but the Xtol was incredible sharp with slightly larger grain. If you’re looking to get a little bit more speed for low light without changing the negative characteristics too much, this is a nice combination.
If you’re looking for maximum speed for low light, try Ilford Delta 3200 pushed to 12,500. Develop for 16.5 minutes at 20 degrees C in Ilford Microphen (stock solution).
If you just want a little more grain, you can shoot as normal at the printed ISO, and then use higher developer dilutions to get more grain. Microdol-X (stock) will give less grain than Microdol-X (1+3), for example.
You can also pull film by 1/2 a stop, and use stock or higher dilutions to get interesting looks. And for the coolest grain (like sandpaper) of all, try Delta 3200 at 800, develop in Ilfosol-S (1+9) for 8 minutes at 20 degrees C. Delta 3200 has enormously wide exposure latitude; it is actually rated at around 1250, but it is designed to be pushed. So ISO 800 is about 1/2 stop pull from the rated speed.
There’s a thousand combinations of film and developers, have you see the Massive Dev Chart at http://www.digitaltruth.com?