I'd separate the cold sends onto a dedicated sub-domain like outreach.yourbrand.com and warm it up really slowly - even a couple of hundred messages a day is fine as long as you build from a low base and ramp up gradually. Rush it and you'll see hard bounces and spam-trap hits that can poison the whole root domain, and nobody wants that.
Four inboxes can work if you rotate them and keep each under about fifty messages a day, but adding a couple more gives you breathing room and lets you segment coaches vs directors with slightly different copy - makes the outreach feel more personal.
For EU-focused B2B I've had good results using a warm-up feature from Instantly combined with a simple sequencing tool like Lemlist, which handles GDPR-compliant unsubscribe handling out of the box. Expect reply rates in the Nordic market to sit around two to four percent - the usual benchmark isn't far off. Keep the cadence tight: a handful of touches over two weeks, so you stay within that one-to-two-month window without over-sending.
One thing I always tell clients: make sure you have a separate sending domain for transactional mail like password resets and onboarding. That way if the outreach sub-domain takes a reputation hit, your paying users' critical emails stay safe.
