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Just guessing, but that hump behind the hammer looks like it belongs on a rolling block pistol frame and the upper tang straightend out. Lower tang could have been swapped out and a standard #2 lower tang installed. 

Almost forgot...I don't remember ever seeing a round-top receiver ring on a factory Rem #2, only ones I ever encountered were octagon.

jimmy wrote on Mar 25^th, 2011 at 4:37am:

I have a #2 that has a round receiver ring. It was originally chambered
for 32-20, and has a rotary extractor. If I can get a photo
for you, I will post it. I have to use my phone, which poses
a few problems

MikeT,
The quick give-away is that the Rem #4 frame to butt stock line was squared, no curved radius at the rear. Also, the #4 didn't have a lower tang, or a removable trigger guard. 

jimmy,
A foreign remake of the #2 keeps making more sense the more I look at the pictures and see additional details that don't quite match up  with the Rem version. 

Shorty, 
Hope you are able to post that picture of yours. You've got my curiosity up. 

Regards to all,
BP

Unless this is some rare prototype of the Rem. #2, my guess is it's an import and the Rem. patent markings are there because they paid Rem. a royalty to build copies of the Rem. #2 and import them here. 

 Strange #2 there in the round top. I was expecting to see a very early production model, as that would make more sense to explain a round top. But the patent dates on the receiver indicate a mid production model with the 4 patent dates. I'd be curious to see the barrel rollstamp to narrow it down further and get an idea as to when it was produced. 
The rotary extractor indicates a mid production also, as early had a fragile thin sliding extractor, and late went back to a sliding extractor, but heavier.
The receiver has been heavily polished and hot blued, so no way to tell if it was always round top at this point, but looks like it might be original.

Thanks Shorty! Very unusual gun, and I wonder why Rem. would begin the #2 with an octagon action, and end it with octagon, but slip some round top in the mid production range (as verified by the extractor)??? 
Like many other makers I suppose Rem. would special order for a customer if he was willing to pay the price, so maybe someone just didn't like the looks of a octagon top and special ordered a round top.