Strictly speaking, the old school of rAgams go by the grAma mUrchana system, so an arOhanam avarOhanam might not cover everything possible on ascent and descent (what exactly is the difference I shall write about after asking musicologists).
Aro : S R3 G3 M1 P D1 N3 S
Avaro : S N3 P D1 M1 M1 G3 M1 R3 S (That's out of the SSP)
The rAgAs of the 6th chakra all have nATa-ish characteristics, and this one even has a MGMR combination too. Other phrases include SMR-SNP (again nATa ish), SDPD, MGMPM-GMRS, SNPDMP, RMGR and more extreme ones like SMPMR. SNDP and SNPDP are both there as well. DPDM is also possible. PDMG is a key phrase that could do with more appearances.
The sole kriti of Muthuswami Dikshitar in gangAtarangiNi is varadarAja avAva - and Amritha Murali's version follows the SSP notation (of course, in a modern setting) :
https://www.youtube.com/watch?v=2jEg8OWvWF0 - as I thought, the nATa DNA is strong in this one as well. But then the rAgA distinguishes itself with the D1
A search on sangeethapriya reveals another composition, sArasa nayana in gangAtarangiNi by Ramaswami Diskhitar (Muthuswami Dikshitar's father for who do not know, and a phenomenal composer who needs to be heard more) in this lec dem by BMK here (demonstrating both swara and sahityam, so it's your lesson of the day

The is actually a type of composition called a daru. It starts on a prominent swarAksharam and it seems like RD has used SNDP and SNPDP also, along with SRS-MGM - the Dikshitar style that runs in the family is distinctly seen here. This is the only available recording of it, so please save it.