Yes you can do it. I do it with 4 different devices all using the same Apple ID.
You need to associate different email addresses for each device in order to use those email addresses as the "contact at" email address. The reason the calls are dropping on you now is that what you are trying to do is like calling yourself on your own phone.
You can also create new iCloud accounts on each device simply to use for FaceTime, but I'm guessing that the users of the other two devices have their own email addresses which will make this work for you quite easily.
Take a look at this for more information.
http://macmost.com/setting-up-multiple-ios-devices-for-messages-and-facetime.htm l