I have a particular project area that i would like to apply a band equation to a specific area and a different equation to another area. I am using the API function and would like to know if two “geometry” parameters can be called or how i could segregate the analysis in a single call.

My alternative is to run the API twice (one for each area of interest) then combine the two tiff outputs, but this is a little messy.

No, this is unfortunately not possible. Nobody came up with this idea yet…
At the moment most of the analysis is done per pixel in spatial terms, allowing to go through temporal and spectral dimensions. I am not sure how this would work with two geometries.

If you need a comparison of the areas in a statistical terms, you can calculate statistics for each of the calls (see Tip 9 in this blog post) and then compare these.