How much do you have to spend?

IMHO, diminishing returns applies more to electronics (assuming those electronics are not flawed) than to speakers and phono cartridges. Speakers affect the sound  more than any other single component.
I own Ref 3’s, upgraded from R11’s. While a similar overall sound, significantly cleaner & clearer & well worth the investment. Speakers should IMHO be your largest investment by far, with substantially less diminishing returns. 

I don't know much about NAD, or never heard anything exciting about them that would make me try them. KLH speakers, yes, but I agree with the comments above, it's a too many tricks pony, it would be first to replace on my list.

Naim Uniti Atom all in one everything,$3500 do $3500 for speakers you are done if you stream only..

Very happy that I paired a HIROSE RS-520 with the Cornwall IV's. The capability of the RS-520 will meet audio needs for years possibly decades to come. 250W with Klipsch speakers is a bit of an overkill but the HIROSE is extremely clean. Highly recommend it. The combo is a simple one and done setup. 

I wouldn’t spend $10k on new speakers if you’re planning on keeping the NAD.  Also, I’d buy Joseph Audio Pulsars over the KEFs, but that’s a personal preference thing.  Just my $0.02 FWIW, and best of luck.