In the other thread on dhanashree, I mentioned that it was a HM rAgA imported down South, an ancestor of bheemplAsi and the version we see in CM belongs to the kAfi thAT.
There is another dhanashree - of the bilAwal thAT as well. It uses G3 and N3. For this reason, I am taking a quick detour to HM rAgAs for this post.
A recording of this comes from First Edition Fine Arts Channel - https://www.youtube.com/watch?v=PXI675MJoZ8
PS - A brief note : HM uses a system of thATs that's not unlike the 19 original asampUrNa mElAs of Venkatamakhi in its concept - in fact it was Pandit Vishnu Narayan Bhatkhande who borrowed the idea from CM and took it to HM where he wrote the first modern treatise on HM. Prior to that, HM had used a rAga, rAgiNi, and putra classification.
HM rAgAs in general are very old school, and given the history of North India, come from a much larger base of diverse regions and traditions, with many different origins -- the CM rAgAs that have gone to HM are only the latest installment. They liberally use non-linear phrasing, extra notes and the like. There are often many different versions of one rAgA, and there are cases where the same rAgA might have different names in different traditions, or different rAgAs with the same name as well. Its far more lakshya based even today with plenty of "mishra" versions. I am not very familiar with HM, but it looks like the decline of the gharaNa system (once fiercely guarded like ancestral wealth) has given musicians much more exposure, caused many of these traditions to mix, but many other traditions and schools might have gone extinct over time. That's about as much as I know.
CM too might have been like this in the distant past (we have similar things going on with our rAgAs, but far less overall), but because its far more codified down and South India hasn't seen as many influences and changes as HM did in the turbulent middle ages, there is more clarity about the lakshanas and the past history of CM rAgAs now. In present day CM, the modern school (coming from Govindacharya and leading to the sampUrNa mElas and modern versions of rAgAs) and the old Venkatamakhi school (the asampUrNa school upheld by the Dikshitar Family) are the 2 major points of origin of the CM rAgAs in vogue currently, along with old tamizh music and the rAgAs imported from HM.