Specifically, between MathOverflow and math.stackexchange.com. Similar to http://meta.stackexchange.com/questions/2928/move-questions-between-se-sites, which asks about moving between MathOverflow and StackOverflow.
Today, the private beta for math.stackexchange.com began, which differs from MathOverflow in that it covers more basic topics. In the past, questions have been deleted from MathOverflow for being too elementary. Soon, there will be someplace else for these questions to go.
Research-level questions that get asked on math.stackexchange (less likely) could potentially also be moved to MathOverflow. Has any progress been made since the last question on this topic as far as allowing the importing/exporting of questions on stackexchange sites?