If you have "all the legal coverage of music to be played" then you would have no reason to be posting a question. So perhaps you do not have all the coverage.
Without reading the iTunes terms of service, I am guessing you have bought a license to play the songs privately. That means you, your family and casual visitors to your house. But now you plan to have public performances and that requires a separate license. Well, yes, it is another way to collect money. BMI, in behalf of its performer-clients wants a piece of your action.
The problems are two: that you are probably not licensed for public performance through iTunes and that would be a copyright infringement, and also that BMI has become aware of you and may well sue if you do not pay. And ASCAP and SESAC may be close behind.
As I said, though, the deal on the joke box is whatever the contract says it is. You can either pay BMI or, if it is enough money to be worth it, have an attorney who does entertainment or copyright read the jukebox contract and figure things out for you.
Licensed in Maryland with offices in Maryland and Oregon. Information here is general, does not create a lawyer-client relationship, and is not a substitute for consulting with an experienced attorney on the specifics of your situation.
Another example of the folly of proceeding without a lawyer, this time on compulsory copyright licensing.
Q: "We have a ITunes juke box which has all the legal coverage of music to be played"
A: Oops, neglected the key word at the end PRIVATELY.
As Attorney Marcus has just explained you don't know what you think you know, which has you in a pickle with Broadcast Music Incorporated (BMI) which caught you broadcasting music without a license to do so. There are 3 main organizations that give blanket music composition licenses, BMI, ASCAP and SESAC. BMI is the one that caught you infringing. You need to call one of the 3 and get that blanket license if you want to be broadcasting music over your sound system to the public.
I mean, really - do you think you can buy a song on iTunes and then blast it out legally over the PA at the SuperBowl without any further license? Not a chance.
However, good news for you is the license is routine formality and the license gives you rights to broadcase anything from their entire catalog of songs from the 550,000 songwriters they represent. So, just get the blanket license and get off your know-it-all highhorse before you get knocked off by one of the big 3 licensing houses. They won't let you slide for long.
I am not your lawyer and you are not my client. Free advice here is without recourse and any reliance thereupon is at your sole risk. This is done without compensation as a free public service. I am licensed in IL, MO, TX and I am a Reg. Pat. Atty. so advice in any other jurisdiction is strictly general advice and should be confirmed with an attorney licensed in that jurisdiction.
I represent several digital jukebox companies.
You need a license for the recording from the record label. Your iTunes purchase does not qualify.
You need a license from each publisher on each song on your "jukebox" and some songs can have up to 22 publishers on a single song.
Plus you need a license from each of the 3 performing rights societies, ASCAP, BMI and SESAC. Assuming you are operating in the USA.
This post does not create an attorney-client relationship between my firm and the asker. In all events, the asker is well advised to secure advice from an attorney with experience in the area covered by the question asked. This answer is posted for general purposes only.