multivitamin necessary for breastfed baby?

3litttlebirds

I should start out by saying that my baby was a preemie , born at 34 weeks. However, he has not had any health issues. When he was discharged from the NICU, I was told to continue the Poly Vi Sol with iron multivitamin. I've been thinking about it lately and wondering if he even needs the multivitamin as he is EBF. I have been doing some research and there seems to be conflicting information, particularly in regards to whether or not vitamin D passes through breastmilk.

I realize that my situation is different given I had a baby that was a preemie...but, in general, what are your thoughts on given EBF babies a multivitamin? Particularly, what is your knowledge on vitamin D supplementation?