In my experience Alligator is a basic indicator and it can be use with several indicators. In fact, there are many strategies based in Alligator signal confirmation. Fractals and Resistences & Sopports Levels are the most popular mix of indicator that can use an Alligator’s principles to build a successful strategy in the market.
For example, as you see in the figure, I follow Alligators downtrend signal confirmation. The Alligator’s mouth is wide open and the price has already broken the support level at 1,42754. As my trendline support has been also overtaken I can anticipate the price is heading towards the pivot at 1,40345 level. That way I set a selling stop just below the trendline and another one in between the pivot and the first resistance.