I think you pose a good question. No question there are lots of possible answers. My thinking is you first want rock solid basic electronics… the preamp / amp. This will give you solid - detailed and realistic output from whatever your source is and what ever your speakers are. I think the Parasound would be a very substantial upgrade and take hold of the speakers downstream and get the most out if what is coming from upstream.
Typically, the best way to upgrade is to look for weaknesses and bring them up to the level of the rest of your system… then once you have achieved parody of all your components, enjoy for a long time. Then reach for the next level… never invest less than 2 times in a component upgrade.
So, looking at your system… first amp, then preamp… getting the Anthem out of your system. When you have a higher level preamp and amp… then start thinking about what should be next.