My favorite solution to the breakdown of correlation is to have order books for beta adjusted prices. That is, you don't bid for Google stocks, you bid for a Go

My favorite solution to the breakdown of correlation is to have order books for beta adjusted prices. That is, you don't bid for Google stocks, you bid for a Google stock minus an equivalent amount of S&P. The price of this pair is much more stable than the price of Google, which means spreads can be tighter. The nuttier generalization would be to have an order book for each principal component of the covariance matrix of the market. It wouldn't work in practice for a variety of reason (least of which is that the covariance matrix is unstable, ill defined, etc) but it's a good thought experiment to understand the problem.