Greycroft, the New York and L.A.-based venture firm founded in 2006 by investors Alan Patricof, Dana Settle, and Ian Sigalow, has closed on two new funds totaling $678 million in capital commitments. One of those funds is its sixth flagship early-stage fund and it closed with $310 million dollars. The firm also collected $368 million in commitments for a third growth-stage fund that it will use to support breakout startups from its early-stage portfolio. The venture fund invests between $500,000 and $10 million in a first check, and Greycroft will…