I was in my home country one month after finishing my first and got the second. I'm sure there must be some limits somewhere. Probably different in various embassies.
If you bring a "letter of reference" from your embassy (in some cases it's just a certified copy of your passport), it'll be easy. I used Bangkok Bank in EmQuartier (Phrom Pong bts).
Been having similar thoughts :) They must make up some unique key. But then when John Smith out of the uk arrives with a new passport, it must take some time for them to look him up.