It really depends on the sensitivity of the dog in question & how similar the formulas are within the same brand. Many brands have very similar formulas with just a change in the base protein (they will often advertise that they are created for 'rotational feeding') As long as the dog doesn't have any particular sensitivities to different proteins, and/or physical digestive issues that cause problems with variety, then I'd generally say that the more you switch up foods (both protein and brand) the easier the transition will be going forward.
One thing to keep in mind is this - most brands use a 'premix' of added vitamins/nutrients which is used throughout their brand, regardless of formula or primary protein. Rotating within a single brand doesn't protect your dog from deficiencies caused by limits in that particular premix. Best case scenario is to rotate both protein AND brands, so you're getting a (potentially) better coverage of all micro-nutrients included in the kibble, which will differ - often greatly - between brands.
One thing to keep in mind is this - most brands use a 'premix' of added vitamins/nutrients which is used throughout their brand, regardless of formula or primary protein. Rotating within a single brand doesn't protect your dog from deficiencies caused by limits in that particular premix. Best case scenario is to rotate both protein AND brands, so you're getting a (potentially) better coverage of all micro-nutrients included in the kibble, which will differ - often greatly - between brands.