Like Goldman Sach's private stock exchange? Sure, but as they grow they run into the same problem as public capital markets. Eventually somebody prominent gets screwed, they make a big stink about it, and the government regulates them as if they were public.
This is basically the story behind investment trusts, mutual funds, and hedge funds. Back in the 20s, everybody put their money into investment trusts. They got screwed by the Great Crash, so the government put all these restrictions on public investment vehicles (can only invest in stocks & bonds, can have no more than 1.5% of assets in any one security, etc.) and the trusts were reborn as regulated mutual funds.
Then people realized that because mutual funds were so regulated, they were leaving money on the table, and all these alternative asset classes like commodities, timber, derivatives, venture capital, etc. were ripe for the taking. So they created a new class of investment vehicle, hedge funds, without the regulations but only open to people who supposedly know what they're doing.
Now ordinary people are investing in hedge funds indirectly, through funds-of-funds and pensions, and they're getting screwed. So there're calls to regulate hedge funds now.
Financial markets treat regulation as damage and route around it. Unfortunately, they sink many suckers in the process and create demand for new regulation, and so on.