3 ring gag with 2 reins?

No, with roundings you will lose the refinement - the bottom rein should only be used as needed, the same as with a pelham.
 
The snaffle is the mouthpiece and the 3 ring is the cheekpiece. In fact a three ring gag is not a gag at all. Unfortunately the three ring gag gives horses a very confused message - especially as most people do ride with only one rein. The snaffle, especially when single-jointed, asks the horse to lift his head and the the lower rings, especially the third one, ask for the horse to lower his head. Often people combine this with a running martingale which also says lower the head.

Obviously I don't know why the OP is considering a gag in the first place and of course safety must come first, but there are a lot of bits out there which give a better, clearer and kinder signal to the horse....might be worth experimenting with different mouthpieces (which are for the horse) and cheekpieces (which are for the rider).
 
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