For powering something like the Kemper, I really like the PowerStage 700 (or even the PS-200).
Plenty loud, plenty of headroom, doesn't sound cold or sterile yet doesn't alter the tone either.
Used it with both Fractal AxeFX as well as with a Helix and worked equally well with both.
Even used it with regular stomp boxes and still sounds pretty convincing (especially when using the 200).
In terms of other good solid state amps I've been digging, was really surprised at how much I liked the Fender Tone Master Deluxe Reverb.
Was surprised at how convincing the modeling was in that. For people who are used to using Fender tube combos and looking for a viable
SS alternative, I really suggest checking that one out.