There are days that I think that I have a hobby of 'collecting' brokers.
I've been up to 4 different brokers before, and have multiple accounts within them.
Sometimes I use a different account at the same broker, or a different broker - for money management reasons. There are some brokers I use (
such as Sharebuilder) purely for investing, and not for trading. Other brokers (
such as Scottrade) are difficult, if not impossible to invest with - since they don't offer DRIP's. But they're ok, as far as trading goes.
So to answer your question - yes.
And I know quite a few other traders and investors who do the same thing I do ...