This would do the trick with any shell:
tar c myfiles | gzip -cf9 | tee backup.tar.gz | gunzip -c | bzip2 -9 - | ssh 192.168.0.4 'cat > backup.tar.bz2'
But admittedly there is some overhead involved ... :-)
There are tricks with bash and probably other shells that
will let you avoid some steps above, that has already
been shown in another comment.
Well, I see your point though. I don't know if it's really
worth adding those features to the shellpipes, but if you
really think they would be useful then why not add those
features to your favourite shell? Or perhaps just make a
helperprogram that does it.
The beauty of Unix and its commandline interface is really
how one can accomplish complex things by combining several
small and simple standard programs and the builtin
features of the shell. And if something is missing, you
can add that something yourself (if you can code).