As said above, the most significant thing you can do is be careful with foot placements, both in terms of avoiding rock or in judging the angle and pressure just right. But there are often situations where you have no choice, so...
I have had boots of greatly varying 'stick'. I have to admit that there has been a strong price correlation to this, but that could have been a side effect of the other correlation where the more of a mountain boot it was, the better. For instance, my La Sportiva Guides were much better than my Brashers whatevers.
The grip level of any boot can be improved to some degree by roughing up the surface of the soles with sandpaper. The obvious penalty for doing this is increased sole wear and reduced longevity.
This brings me to another very important thing. Before the soles are poured into the mould, there is a non-stick layer applied to it to make it easier to get them out again. Sometimes, this comes off on the sole rather than staying in the mould. So you can get one pair of boots that stick well and another pair from the same batch like greased lightning. Sanding this off can make a world of difference.