This "add up" sounds awkward, as it sound more like arithmetic expression, but does it just mean "increase"? Does it sound natural?
ex)A situation may seem familiar because it is similar to other stored events. For instance, imagine you are shown pictures of my family. Afterward, you happen to see me and think that I look familiar. Although nobody in my family looks just like me, the similarities tend to add up.
No, the similarities do not increase. They build up into a model. They aggregate, accumulate. Each similarity adds to the next/last one. None of the similarities increase.