Roman triumphal arches (fornix, ianus, then arcus triumphalis) are generally categorized into two main types: those with a single arched opening (e.g. Arch of Titus) and those with three openings (e.g. Arch of Septimius Severus), though exceptions such as the four-way tetrapylon (arcus quadrifrons) in Leptis Magna also existed.
What I am curious about, and have not been able to find a satisfactory answer to, is whether there existed some sort of developmental pattern between the two types. By sheer enumeration of extant Roman triumphal arches, it is clear that those with one opening are far more common, but that result may simply be a reflection of the fact that three-arched arcus were more elaborately decorated with pictorial reliefs, thus requiring more resources to construct.
In terms of typological development, it is not clear to me whether the two types were related iterations of a shared prototype, or rather had dissimilar origins. This question could be further broadened to an inquiry into the architectural origin of Roman arcus triumphalis.