Apparently you can do this with Home Sharing (http://support.apple.com/kb/HT3819). Initially you will need to use the same Apple ID across all devices to download the apps you want to share. Once they have been downloaded and authorized, you can then sign in with a different Apple ID and use the 'shared' apps fine. I have not personally tried this, but there is plenty of evidence that this works from scanning a few Google search results.