I want to remove all six cogs from an atom 77 compact freewheel for cleaning. I was able to unthread the smallest one from the body and then the next two were splined. It looked like the fourth one was threaded to the body. I tried to unthread it by turning it counter-clockwise with two chain whips but it would not budge. Anyone have experience with these freewheels who can advise me? Thank you.

I don't have specific own experience with this particular freewheel, but I found a picture
https://www.velo-pages.com/main.php?g2_itemId=22673 , which confirms your assumption of a second step on the freewheel, which again is locked by a threaded cog.
It has been my experience in general with dismantling freewheels, that you have to use the two chaninwips in a way that they form an X to take full leverage advantage (see picture from Park website)

As above, I'm not familiar with that particular freewheel but I recall reading about some where the largest cog was threaded on and had to be removed to access the adjacent ones.