To allow a number of App Services to scale independently I needed to pull one of them out of an App Service Plan where it had lived with 3 others to sit in it’s own plan – experience had shown me that it’s scaling characteristics are really quite different from the other App Services.
You can do this straightforwardly and pretty much instantly either in the Portal (there’s a Change App Service Plan option in Settings) or with PowerShell (with the Set-AzureRmAppServicePlan cmdlet).
Super simple – but I did encounter one gotcha. This doesn’t move any deployment slots you might have created and so you end up in a situation with the main App Service sat in one App Service Plan and it’s deployment slots in another which probably isn’t what you want and, in any case, Azure won’t let you swap slots in different service plans.
The solution is simple: you can also move them between App Service Plans in the same way.