What you think about remarketing system like AddShoppers?
I have experience with AddShoppers and beside high onboarding fees after couple of months you can reach the values around 3 to 1 ROI with only commission fees. They provide exclusion list so you can easily exclude you active email marketing subscribers to not cannibalize revenue form Klaviyo.
Also with good offer and additional personalized flyout or popup you can enrich Klaviyo audience.
Did you use it for you brands? Maybe you have some other you can recommend?