A grade beam approach goes as follows:
Let us assume that you have a physical eccentricity of 0.5 ft and an axial compression of 200 kips. So, you need a moment of 0.5 ft x 200 kips = 100 ft-k to counter this eccentricity. You must then add a grade beam that connects this footing with a column/footing located in the opposite side of the physical eccentricity (i.e. towards the inside of your plan view if the footing of interest is close to the property line). The grade beam must be capable of carrying the moment of 100 ft-kips. The grade beam will also transfer a moment of 1/2 x 100 ft = 50 ft to the opposite column generating a smaller eccentricity (in the opposite direction) to that column. Typically this should not be an issue (smaller moment, larger axial compression to an interior column). However, it is best if you extend the grade beam to the next column, which will now have to carry a moment of 1/2 x 50 ft-k, and so no. The idea behind this approach is that your footing tends to rotate toward the side of eccentricity. This tendency activates the resistance of the grade beam, which now develops a counter moment, thus reducing the effects of the physical eccentricity.