I've often found a situation where multiple replies helped with an answer, but only one person gets the overall answer. I think it would be incredibly beneficial (and fair) to provide a function to say an answer that was provided "assisted" as well as being able to tick just one as the current "answered the question".
I don't think this warrents the additional UI complication - it seems like this is basically what upvoting is achieves - the most upvoted answer will be displayed just below your accepted one.
There is nothing prohibiting you from upvoting multiple answers, which I think would be more than enough to reward an answer that provided extra information (or was also factually correct).
I’d like to point out an example scenario which demonstrates the utility of assists. In this question, I asked for help to correctly get a command-line argument. The two posted answers were not useful, but the two comments (to the question itself) did give me a nudge in the right direction. As a result of the two comments, I did some testing and found the solution myself. I figured the correct action to take was to post the final answer myself since none of the existing answers were applicable. However, the most that I could do to credit the two people who helped (ie assisted) was to up-vote their comments.
I believe that an assist feature could be helpful in the this situation—like ExpertsExchange has—(though I’m sure that someone can probably explain why even in this scenario it is unnecessary).