It sounds to me like they want to recreate the
Peershares platform. Each Peershares implementation runs on its own blockchain. Businesses can create their own Peershares implementation and raise funds by issuing equity or shares to people who purchase them. Any profit made by the company can be distributed to all shareholders in the form of Bitcoin, Peercoin or any crypto they want to use. All shares in a company are also tradable just like any other crypto.
NuBits/NuShares already use a heavily customized version of Peershares and the upcoming
B&C decentralized exchange will use it as well. It's not necessary to customize it though. It can be used by a business just as a way to sell equity and distribute dividends. Nu has made some great advancements to Peershares as well, including decentralized motion voting and data feeds which allow a user to subscribe to another person's voting feed in case they're too busy to keep up with the news. Another upcoming feature is the ability to vote to offer new shares, which means the supply can always be increased at the will of shareholders. It would dilute existing shareholders, but it would allow them to sell the new shares and raise more money.
What's important here is that it lines up with this...
One word: control.
Regardless of how much PB loves BTC, the Overstock board is not going to place an important part of their future business strategy in the hands of a 3rd party.
Overstock will create their own blockchain for the Medici project, the only real question is what they will base it on.
Using Peershares, they're not dependent on Bitcoin, NXT or any other 3rd party blockchain. They control their own.