The other John Brunner book I read recently was Meeting at Infinity (copyright 1961). I quite enjoyed it!
I quote the summary on the back of the paperback in full, because (as was common for this era) it has very little to do with the actual plot of the book. Enjoy!
In an infinity of parallel worlds, many are the inventions which would paralyze less advanced worlds. And one such invention was the one the noted physician Jome Kenard used to restore life and senses to the injured beauty Allyn Vage.
His strange machine had been imported from a seemingly primitive people on the world of Akkilmar. It worked -- but its workings were incomprehensible even to Earth's best scientists.
Nevertheless, once used, the doctor and his patient had been transformed into the lever that could topple a world!
(One thing I notice about this is that there's no character named Jome Kenard in the book. But I nitpick.)
The basic idea is that a technological way to enter parallel universes has been discovered, and at the time the book begins is ruled by oligarchy of merchants who have divvied up rights to trade with the various universes, which as it happens is a very profitable activity. (I previously complained about a silly plot device used early on in the book. I don't think the device is mentioned after about the first ten pages; at any rate, it didn't seriously reduce my enjoyment of the book.) Since the Earth essentially acts as a middleman and has little if any industries of its own, most people form a large, bored, disenfranchised, and unemployed underclass, who get what they need to live but have little they can aspire to. There are also a bunch of cults running around who want the portals to the different universes shut down.
This allows Brunner to show the world from different perspectives (from the oligarchs, from the underclass, etc.), a task which I think he does quite well. Some of the underclass chapters reminded me very strongly of cyberpunk (there's a bunch of mobs inhabiting the underclass that collect information and try to turn it to their profit, and it's all very cyberpunky even if there are no computers involved).
So I thought there was a nice meshing of a lot of elements, that the writing was good and engaging, and that the plot (I haven't talked about the plot at all!) was fine. Some of the things that happen towards the end are kind of obscure, and I didn't understand what the hell was going on on the last page or two at all, but I'm willing to believe that something profound was going on and I just didn't get it. (This is the level of good will that the novel built up in me!)