The Canon 100-400 for around $1600 would get you IS, but no additional reach and still f5.6 at the long end.
The Sigma 120-400 OS or 150-500 OS also would get you stabilization (some say it's better than Canon's IS)... but still f5.6 or f6.3 at the long end. They sell for $1000 and $1100 respectively.
None of the zooms will have quite as good IQ as your 400/5.6. Though the Sigma 120-300/2.8 OS
might come close, even with 1.4X and/or 2X teleconverters. This would set you back about $3300-3600 US.
Another zoom that should rival the quality of primes is the upcoming Canon 200-400/4 IS 1.4X (built in teleconverter, to make it a 280-560/5.6 by flipping a lever)... no price has been set yet, but most are guesstimating it will be in the $11,000-$12,000 range.
The cheapest super tele prime longer than 400mm is the Sigma 500mm f4.5
. It's $5000 US and doesn't have stabilization.
You might consider a used Canon 300/2.8 IS "Mark I" with teleconverters, it wouldn't be cheap, but will be a whole lot less than the price of a new one. It is one of Canon's best lenses ever and works very well with quality 1.4X and 2X teleconverters.
Canon 400/2.8 IS Mark II is two stops faster (and a whole lot bigger), has IS, and works very well with teleconverters, too. But also is $11,500. A used "Mark I" is still a superb lens, though big, might be found for somewhat less, but still won't be cheap.
Canon 400/4 IS DO is one stop faster, has IS, is a bit smaller... is currently selling for under $6000 US. I haven't used it, but supposedly the Diffractive Optics don't work well with teleconverters.
Canon 500/4 IS are smaller than the 400/2.8s, but not as small/light as the 400/4 DO. The 500/4 IS Mark II is $10,500. The 500/4 IS "Mark I" is still a great lens, might be found for a bit less used.
600/4... 800/5.6... well, you get the picture. Sigma also offered an 800/5.6 at one time... I don't know if they still do, but I don't think it ever had OS either.