The way most digital nomads (including myself) approach this is to not be an employee, but rather a contractor. I'm an Australian and run an Estonian company (it's far from the only option, but they make it very easy). I invoice my customers for long term contract work.
Assuming your large corp / HR are friendly, they might even be willing to switch to a contractor relation (depending on the juristiction this might not be allowed, e.g. Germany is very tough on contractors as employees).
This prevents the biggest problem of large corporates. Being in the country with employees might make you a 'permanent establishment' and therefore liable for local tax law.
Worth looking into Estonia's e-residency program and suppliers like xolo.io (The leap product, not the Go product).