'+>>' is not listed in the open docs, so I wouldn't use it as a supported option. I don't see why you couldn't use '+<', as that is listed in the docs. After opening the file, you can read from it, and/or seek to the end of the file for appending.

Update: I take it back, I do see '+>>' in the docs, but you would then need to use seek to read from the beginning of the file, as already suggested.