I answered, "I have another one percent." Is this wrong?
I think it works.
There is a different nuance between your sentence and theirs. "I have one percent more" is comparing what I have to something else. But "I have another one percent" is not necessarily a comparison.
Yes, it is incorrect grammer.
yesh li od achúz echád.
I wrote "I have another one percent" just to please the trolls upstairs. But, I think the real translation is "I have another percentage point."
When I transferred earlier "I have one more percentage" it was not accepted. Here this sentence is used.
The rule for using percent and percentage is...the word percent (or the symbol %) accompanies a specific number, whereas the more general word percentage is used without a number.