The last year most major record companies have resorted to what's known as a "360 deal," which is an agreement that allows the record label to share in all the money generating possibilities of an artist's career, from touring to publishing to merchandise sales income.
Many desperate new artists signed a 360 last year, only to find out later that a label had no expertise in anything other than selling your music (and even that expertise is dubious these days). If things went sour (as they frequently do) in the older record-only deals, a label could freeze a record from coming out, but the act could still make money by touring. In a 360, the label can effectively stop the artist's career in it's tracks!
There's no wonder that management is advising clients against such deals unless it involves a boatload of money. As a result, some enterprising label lawyers have come up with a new name to try to soften it a bit - a "multiple rights" deal. Same thing, different name.
Of course, management has a built-in bias against these deals since the language frequently includes such gems as "the artist must limit the amount of commission you pay your manager". The label, in effect, wants to be your manager, which is great incentive for any artist to stay as far away as possible from the major labels these days.
So to summarize:
360 + no $ = run far away
360 +$ = run far away
360 + $$$$$ = think about it strictly as a money deal, but understand it could be a death blow to your career.