Dual Citizenship - Georgian Passport

So you mean it is well possible to keep your current passport while you get a new one from Gerogia?
If Georgia becomes aware that a Georgian citizen has obtained another citizenship, it could strip him of Georgian citizenship. But they can’t check if one has renounced other citizenships or force one to become stateless while waiting for his Georgian citizenship.
 
Yes, so what you can do is getting a Georgian one while renouncing your current citizenship. You can then apply for your previous one again right away, depending on your citizenship. There are quite some countries (notably UK) having procedures for exactly for this case. But please note that you would have to request retention of Georgiran citizenship:
https://matsne.gov.ge/en/document/view/2342552?publication=8

I guess, they won't catch you, but it is not exactly honest. Same goes for Austria, for example.