Seeing as there is nothing physically standing in the way of you doing this, and it is a completely subjective topic (one fraught with emotion, it seems), I am going to offer my opinion:
Can I post the same question to multiple sites?
Yes, technically there is nothing stopping me.
May I post the same question to multiple sites?
If Jeff Atwood had his way, perhaps not. But even he is not stopping me.
Should I post the same question to multiple sites?
That depends on a number of factors:
Am I responsible enough to follow up on the same question on all sites? In other words, would I make sure to go back to each one and follow up with the people who answer? If I get a satisfactory answer from one instance of the question, would I go back to all the others, and provide a link back to the answer that helped me and inform other readers thereof (as opposed to just leaving them to rot)?
If I can answer yes to the these questions and follow up in a responsible manner, then surely there is no reason why I shouldn't post the same question to multiple sites.
If, on the other hand, I was just a taker who wanted a quick answer and never followed up with the people who spent their time and energy reading the question and answering it, then I should not be posting my question to multiple sites.
It would help if, in each instance of the same question I post, I also add a note and link saying where else I have posted the question.
Another facet brought up in another answer to this question is whether the sites have the same users and whether in fact I would be wasting my and other people's time by posting to different sites. That too could be a deciding factor.