The most straightforward meaning of 기도 하다 seems to be 'and' or 'also':
좋기도 하고 나쁘기도 하다 => it has both good and bad points
한국 전쟁은 "육 이오"라고 불리기도 한다. => The Korean War is also known as (the war of) "June twenty-fifth."
I have been told by a native speaker that it can sometimes denote alternatives, and this page on howtostudykorean.com has some examples:
저는 그 친구를 좋아하기도 하고 싫어하기도 해요 => I like that friend sometimes, and I hate him sometimes too
제가 나갈 때 가끔 향수를 뿌리기도 하고 가끔 안 뿌리기도 해요 => When I go out, sometimes I put on (spray) perfume, sometimes I don’t
These cases can be seen as alternatives, as they contain two opposite meanings - But as the howtostudykorean page suggests, you can still think of the function as additional : there are these cases, and there are these cases (similar to the previous 'it has both good and bad points' example).
I still wonder if some cases are ambiguous. For example:
자전거들 예쁘기도 하고 빠르기도 하다
Does this mean that all the bicycles are pretty and fast? Or could it mean that there are some pretty bicycles, and some fast ones?
If that case is not ambiguous, are there any that could be?