Several options, would require thinking through them. Not something we'd typically do but I love a good challenge, happy to lend input and help you work through it if you want.
First thing to keep in mind is that our Soundstage™ systems replace and amplify the front speakers only (underseat, midrange, and tweeter). This is an overview of why (
https://integralaudio.com/other_files/The%20Evils%20of%20Rear%20Speakers.pdf, but the short version is they should be doing 90+% of the work, and focusing your $$ there gives you the biggest improvement in sound quality. In general, for a particular amp topology, power density is relatively constant so for a given footprint you're looking at the same total output regardless of the number of channels you're diving that power over. You get much more benefit throwing that power where it is needed - front mid/tweet/underseat and true subwoofer - and utilizing the existing factory amplification in places where you don't need more power anyway - center and rears.
All that's a long way of saying you'd need to power the center and rears from somewhere because our Soundstage™ doesn't. Well, you don't HAVE to. If I had a choice between any factory or other aftermarket system with center/rears and our Soundstage™ without, I'd chose the Soundstage™ every time, though I'd still prefer to have them if I could. A lot of purists purposely go only 2-ch. Depends on how much cost/effort you'd want to go thru to keep them.
One possible scenario would be to recode the HU to HIFI so that you've got analog output from the HU, and run that back to the amp from the HU. Use our regular analog Soundstage™ and buy a used HIFI amp. You'd need to make manual connections between the Soundstage HIFI harness and your factory HK loom for speaker outputs. I could source the connectors and terminals for you so that you wouldn't need to cut wire in your factory loom. Our regular Soundstage™ would have all the hardware you'd need, including our relo bracket for the HIFI amp. If I'm thinking about this correctly, you'd to run those 8 analog input wires from the HU back to the Soundstage™ harness, and then 8 output wires into the HK factory loom (via splice or via T-Harness).