There are hosts they do that, but I canīt recommend them.
Just go with M3Server and a VPS Pro, use their latest Black Friday Coupon.
Itīs still valid and also for existing clients, I just asked 10 minutes ago, as I need two VPS Pro soon
https://gfy.com/fucking-around-and-pr...-m3server.html
50% off any vps pro plan for 6 months
Really a good deal.
Ask them to move your sites, even if itīs for little fee, but definitely worth it with the coupon.
But maybe they move free of charge too.... Just ask, Boay.