Yes, Washington, D.C., there is a market where large blocks of stock get traded. It's called Liquidnet.
In April, the average trade size on this "dark pool'' of institutional orders was 43,309. And its participation rate is high. Roughly 700 institutions with about $8.6 trillion worth of equities under management use the network. These mutual funds, pension funds and other asset managers execute big trades between themselves or use the venue's eight algorithms to execute transactions, even if they extend to other venues.