This has been something mountain bikers have been experimenting with for years, so the answer is yes. If your bike is a mullet (29in front and 27.5in rear) you can run a fatter rear tire to close the gap between the diameters but if you want to improve the front-end grip of your bike you can run a bigger tire there too. Bear in mind a fatter tire will have a slight knock-on effect on the geometry; it can slacken the head angle and lift the bottom bracket height.
In most circumstances, a wider tire will offer more grip because of the increased contact patch but in loose or muddy conditions grip is created as the tire digs into the soft surface. A fatter tire can often float over the surface, so in certain conditions thinner can sometimes be better as it cuts through the soft top layer to find grip.