Another more question vs One more question

Some examples from the web:

• Another rule: no more questions, and stop being so polite.
• Another, more general, question is that of the relationship between international and bilateral negotiations.
• There is another and even more important question facing us: can we live in the longer term with common budgetary discipline while at the same time operating different economic policies?
• Another question you need never ask.
• Another question raised relates to the continuation of CFC imports.
• I was asked another question on cohesion policy.
• Let me answer another question clearly.
• Another question is how the EU should react.
• I now have another question for Commissioner Frattini.
• Madam President, I have another question regarding Wednesday.
• They're putting up another question.
• I have another question for you.
• Simply make the false answer another question's truth.
• Actually, I do have another question.
• Let me ask you another question.
• It seems we have another question from the jury.
• Inspector Matter, I have another question.
• Can I ask you another question?/ Sure.
• And when I ask another question...
• Ask me another question, and a hard one this time.

Some examples from the web:

• One more question, I'm jumping in.
• One more question if l may out of curiosity.
• One more question... how does "Hunger Games" end?
• One more question, what kind of sandwich did she have?
• One more question, and then I plunge.
• One more question for the defendant.
• One more question, Mr Madsen.
• One more question about the warning.
• One more question of a social nature.
• One more question, and then I'll leave you alone.
• One more question, and all you little assassins
• One more question, and you go from being the burned spy I hate to the anonymous burglar I shot.
• One more question, something I'm sure we're all wondering:
• One more question: Where do you get good football players?
• One more question for Mrs Fischer Boel: what is your view of such a certification system?
• But I actually had one more question.
• We have one more question for you, Kevin.
• I just have one more question, Detective.
• Wait, there is just one more question.
• Monica, I have one more question for you.