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

You do have the right design—if you want to do this purely within the stdlib.

One thing: instead of teeing to each streambuf on every output, implement it to use the same put area as one of the streambufs it’s given, and copy to the others on overflow and sync. This will minimize virtual calls, which is one of the goals of how streambufs work.

Alternatively, and if you want to only handle stdout & stderr (which is common), run your program through the standard Unix tee program (or the equivalent on your platform), either by doing it yourself when invoking the program, or within the program by forking, setting up the streams as appropriate, etc.

Edit: You got me thinking, and I should know how to get this right. Here’s my first approximation. (When this breaks, you get to keep both pieces.)

#ifndef INCLUDE_GUARD_A629F54A136C49C9938CB33EF8EDE676
#define INCLUDE_GUARD_A629F54A136C49C9938CB33EF8EDE676

#include <cassert>
#include <cstring>
#include <streambuf>
#include <map>
#include <vector>

template<class CharT, class Traits=std::char_traits<CharT> >
struct basic_streamtee : std::basic_streambuf<CharT, Traits> {
    typedef std::basic_ios<CharT, Traits> Stream;
    typedef std::basic_streambuf<CharT, Traits> StreamBuf;

    typedef typename StreamBuf::char_type char_type;
    typedef typename StreamBuf::traits_type traits_type;
    typedef typename StreamBuf::int_type int_type;
    typedef typename StreamBuf::pos_type pos_type;
    typedef typename StreamBuf::off_type off_type;

    basic_streamtee() : _key_buf(0) {}
    basic_streamtee(Stream& a, Stream& b) : _key_buf(0) {
        this->pubimbue(a.rdbuf()->getloc());
        _set_key_buf(a.rdbuf());
        insert(a);
        insert(b);
    }
    ~basic_streamtee() {
        sync();
        for (typename std::map<Stream*, StreamBuf*>::iterator i = _bufs.begin();
             i != _bufs.end();
             ++i)
        {
            StreamBuf* old = i->first->rdbuf(i->second);
            if (old != this) {
                old->pubsync();
            }
        }
    }

    // add this functionality?
    // streambufs would be unconnected with a stream
    // easy to do by changing _bufs to a multimap
    // and using null pointers for the keys
    //void insert(StreamBuf* buf);
    //void remove(StreamBuf* buf);

    void insert(Stream& s) {
        sync();
        if (!_bufs.count(&s)) {
            if (!_key_buf) {
                _set_key_buf(s.rdbuf());
            }
            _bufs[&s] = s.rdbuf(this);
        }
    }
    void remove(Stream& s) {
        sync();
        typename std::map<Stream*, StreamBuf*>::iterator i = _bufs.find(&s);
        if (i != _bufs.end()) {
            StreamBuf* old = i->second;
            i->first->rdbuf(i->second);
            _bufs.erase(i);

            if (old == _key_buf) {
                _set_key_buf(_bufs.empty() ? 0 : _bufs.begin()->second);
            }
        }
    }

private:
    basic_streamtee(basic_streamtee const&); // not defined
    basic_streamtee& operator=(basic_streamtee const&); // not defined

    StreamBuf* _key_buf;
    std::map<Stream*, StreamBuf*> _bufs;

    void _set_key_buf(StreamBuf* p) {
        //NOTE: does not sync, requires synced already
        _key_buf = p;
        _update_put_area();
    }
    void _update_put_area() {
        //NOTE: does not sync, requires synced already
        if (!_key_buf) {
            this->setp(0, 0);
        }
        else {
            this->setp((_key_buf->*&basic_streamtee::pbase)(),
                       (_key_buf->*&basic_streamtee::epptr)());
        }
    }


#define FOREACH_BUF(var) \
for (typename std::map<Stream*, StreamBuf*>::iterator var = _bufs.begin(); \
var != _bufs.end(); ++var)


    // 27.5.2.4.1 Locales
    virtual void imbue(std::locale const& loc) {
        FOREACH_BUF(iter) {
            iter->second->pubimbue(loc);
        }
    }


    // 27.5.2.4.2 Buffer management and positioning
    //virtual StreamBuf* setbuf(char_type* s, std::streamsize n); // not required
    //virtual pos_type seekoff(off_type off, std::ios_base::seekdir way,
    //                         std::ios_base::openmode which); // not required
    //virtual pos_type seekpos(pos_type sp, std::ios_base::openmode which); // not required
    virtual int sync() {
        if (!_key_buf) {
            return -1;
        }
        char_type* data = this->pbase();
        std::streamsize n = this->pptr() - data;
        (_key_buf->*&basic_streamtee::pbump)(n);
        FOREACH_BUF(iter) {
            StreamBuf* buf = iter->second;
            if (buf != _key_buf) {
                buf->sputn(data, n); //BUG: ignores put errors
                buf->pubsync(); //BUG: ignroes errors
            }
        }
        _key_buf->pubsync(); //BUG: ignores errors
        _update_put_area();
        return 0;
    }


    // 27.5.2.4.3 Get area
    // ignore input completely, teeing doesn't make sense
    //virtual std::streamsize showmanyc();
    //virtual std::streamsize xsgetn(char_type* s, std::streamsize n);
    //virtual int_type underflow();
    //virtual int_type uflow();


    // 27.5.2.4.4 Putback
    // ignore input completely, teeing doesn't make sense
    //virtual int_type pbackfail(int_type c);


    // 27.5.2.4.5 Put area
    virtual std::streamsize xsputn(char_type const* s, std::streamsize n) {
        assert(n >= 0);
        if (!_key_buf) {
            return 0;
        }

        // available room in put area? delay sync if so
        if (this->epptr() - this->pptr() < n) {
            sync();
        }
        // enough room now?
        if (this->epptr() - this->pptr() >= n) {
            std::memcpy(this->pptr(), s, n);
            this->pbump(n);
        }
        else {
            FOREACH_BUF(iter) {
                iter->second->sputn(s, n);
                //BUG: ignores put errors
            }
            _update_put_area();
        }
        return n;
    }
    virtual int_type overflow(int_type c) {
        bool const c_is_eof = traits_type::eq_int_type(c, traits_type::eof());
        int_type const success = c_is_eof ? traits_type::not_eof(c) : c;
        sync();
        if (!c_is_eof) {
            char_type cc = traits_type::to_char_type(c);
            xsputn(&cc, 1);
            //BUG: ignores put errors
        }
        return success;
    }

#undef FOREACH_BUF
};

typedef basic_streamtee<char> streamtee;
typedef basic_streamtee<wchar_t> wstreamtee;

#endif

Now, this test is far from complete, but it seems to work:

#include "streamtee.hpp"

#include <cassert>
#include <iostream>
#include <sstream>

int main() {
    using namespace std;
    {
        ostringstream a, b;
        streamtee tee(a, b);
        a << 42;
        assert(a.str() == "42");
        assert(b.str() == "42");
    }
    {
        ostringstream a, b;
        streamtee tee(cout, a);
        tee.insert(b);
        a << 42 << '\n';
        assert(a.str() == "42\n");
        assert(b.str() == "42\n");
    }
    return 0;
}

Put it together with a file:

#include "streamtee.hpp"

#include <iostream>
#include <fstream>

struct FileTee {
  FileTee(std::ostream& stream, char const* filename)
  : file(filename), buf(file, stream)
  {}

  std::ofstream file;
  streamtee buf;
};

int main() {
  using namespace std;

  FileTee out(cout, "stdout.txt");
  FileTee err(clog, "stderr.txt");
  streambuf* old_cerr = cerr.rdbuf(&err.buf);

  cout << "stdout\n";
  clog << "stderr\n";

  cerr.rdbuf(old_cerr);
  // watch exception safety

  return 0;
}