I have a Chase Marriott Rewards Business card with a $30K spend limit on it. I applied for a personal sapphire card and had to call the reconsideration line. They told me that since I had the $30K limit on the business card I would have to shuffle around some credit from business to get the personal card.
I ended off doing this, but I was actually upset about this. My business is legit and I do keep all the expenses completely separate. I explained this to them and said my business credit should have nothing to do with my personal credit. The rep told me that Chase was only willing to risk $30k in credit for me, it didn't matter if it was business or personal.
So, the bottom line, yes you can shift credit from business to personal.