Many of the gods not within the original roman pantheon were often worshipped in a fashion similar or equal to those original ones.

You're probably imagining the idea of the roman pantheon similar to the Greek one. Basically, you have the twelve major deities and that's it. But that was not the case either. Both had an extremely wide group of "minor" gods that were worshipped on similar scale to the main 12 (ex. Aurelian having sol invictus as a patron). Other instances of important minor gods that I've seen in roman art are Roma (personification of Rome) and Victoria. Linked should be some monuments in which these deities were the focal point or shown on the same level to the major 12. http://penelope.uchicago.edu/~grout/encyclopaedia_romana/romanurbs/venusrome.html

https://www.bluffton.edu/homepages/facstaff/sullivanm/titus/titus.html

Another major point is that the Roman religion was not fixed, but rather quite dynamic. This was the case with new additions from roman conquests like Serapis (From the Greco-Egyptian Isis) and Mithras (Similarly from the Greek world). Because of this, Roman religion did not remain fixed on primary worship of the original pantheon.

A subject I know a bit more than worship of Sol Invictus is the deification and cult of the emperors, which can probably present some similarity. Since Augustus, imperial cults were a major mechanism for the emperors to exert influence. As a result, there a plenty of cases where emperors put themselves on similar status to or were depicted interacting deities (I linked the arch of Titus above where he is being crowned by Victoria). Consequently, many of these emperors were worshipped on their own as actual deities typically after their deaths (Madison carree temple). This all suggests that many of these new and foreign deities were worshipped according to their own status without much relation or dependency to the 12 deities of the roman pantheon. Of course, these original deities were important and worshipped a lot. The Gemma Augustea shows this with having Augustus as a deity among these gods such as Minerva and Jupiter. However, these new emperor deities were still worshipped individually and were not fixed in relation to the main 12.

Maison carree: https://en.m.wikipedia.org/wiki/Maison_Carrée

Gemma augustea: https://www.britannica.com/topic/Gemma-Augustea

Source: A history of Roman art by Fred s Kleiner, good overview of Roman art and architecture as a whole and does a good job at examining of emperors attempted to portray themselves