How can I compose output streams, so output goes multiple places at once?

I'd like to compose two (or more) streams into one. My goal is that any output directed to cout, cerr, and clog also be outputted into a file, along with the original stream. (For when things are logged to the console, for example. After closing, I'd like to still be able to go back and view the output.)

I was thinking of doing something like this:

class stream_compose : public streambuf, private boost::noncopyable
{
public:
    // take two streams, save them in stream_holder,
    // this set their buffers to `this`.
    stream_compose;

    // implement the streambuf interface, routing to both
    // ...

private:
    // saves the streambuf of an ios class,
    // upon destruction restores it, provides
    // accessor to saved stream
    class stream_holder;

    stream_holder mStreamA;
    stream_holder mStreamB;
};

Which seems straight-forward enough. The call in main then would be something like:

// anything that goes to cout goes to both cout and the file
stream_compose coutToFile(std::cout, theFile);
// and so on

I also looked at boost::iostreams, but didn't see anything related.

Are there any other better/simpler ways to accomplish this?