I might or might not be an aspie, not 100% sure. But...
I'm fairly good at multi-tasking at work if I have a window open with every thing that needs to be done or a notepad window telling me to do something. Then when I come to as topping point with something I then ALT-TAB through them and pick up whatever seems like a good idea to start next.
When listening to a coworker describe something (computer programming issue) I used to just stare blankly with my eyes out of focus, listening intently, grokking everything. No head nodding, no "uh-huh", nothing. This gave people the wrong impression that I wasn't listening or was completely lost and not understanding anything. After getting annoyed at other people's reactions, I made a concious effort to do the useless motions of nodding and saying "uh-huh". Now I do it habitually all the time without realizing. I don't necessarily call this one "overcoming" because I'm still convinced that it's everyone else that isn't behaving rationally. So I'm stooping down to accomodate their quirks.
For career growth, there was a time when my only next step was to lead a team of programmers. My boss advised me to watch how so-and-so (one of our most successful technical leads) handled other people, helps them with problems, etc. So I did and copied his techniques. For one example, rather than telling someone why he's wrong (which is found to be rude or belittling), using the Socratic method of asking questions so that the other guy is able to reason through it himself and discover the mistake works much better socially. That's one of the few things I observed in the other leader and started using myself. I think that experience has made me very socially adept in an corporate office environment.