We have several employees using the same twitter account (company account) and sometimes it happens that they answer the same question twice.
Do you have this problem? How do you solve it?
Try a Twitter application specifically for business teams, such as CoTweet or Hootsuite.
Split them into shifts?
Edit- hate to give such a short answer but it's simple and it'd work! If you have multiple employees tasked with the same job in any area you'd get duplicate work done. It doesn't make sense to have more than one person tasked with doing the same job at the same time.