I am wondering if the following two sentences have different meanings.
- I may know where it is.
- I know where it may be.
Well, they're not synonymous, though -- depending on circumstances -- they may well describe the same situation.
The first one makes no assertion except possibility, though it invites an inference of some knowledge; the second asserts direct knowledge but limits it to a possibility only. There are plenty of situations where one might prefer one or the other version, but the reasons would have more to do with misleading or tempting listeners than communication.
Oh, and it is definitely the position of may that causes it. Modals are operators, like quantifiers and negation, and they always have a focus, which is determined partly by placement of the modal, and partly by intonation. In writing, with no intonation, this is more complex and leads to a great deal of ambiguity, often among opposites.