My answer is NO if you have your account with one of major brokerage, like Fidelity or Charles Schwab. 

This also depends on individuals.  Someone might sleep better at night if he or she has an account each with two different brokerage companies.  For someone like that, I would suggest to open accounts with no more than three major brokerage houses while he or she has $10M investable asset.  Even though, you have accounts with three firms, it does not mean that all your money are with them.  The reason being is when you buy mutual funds and the money are actually with the mutual fund companies, or you buy individual companies' stocks, the money goes to that particular company, not with your brokerage companies.

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