How to update a cloud service on Azure with a limited user account from the command line
You can deploy, update or delete all of the resources for your application in a single, coordinated operation using ARM.
You would redeploy your ARM template to an existing RG using:New-AzureResourceGroupDeployment
The New-AzureResourceGroupDeployment cmdlet adds a deployment to an existing resource group, including the resources that the deployment needs. This cmdlet is similar to the New-AzureResourceGroup cmdlet, but it works on existing resource groups, instead of new ones. To add a single resource to a resource group, use the New-AzureResource cmdlet.
A good walk through for your scenario (with a few changes) is at: Provision and deploy microservices predictably in Azure
This tutorial shows how to provision and deploy an application composed of microservices in Azure App Service as a single unit and in a predictable manner using JSON resource group templates and PowerShell scripting.
Instead of using an app service resource in the RG template, use the types of resources you'd need. Then call the above New-AzureResourceGroupDeployment cmdlet instead of New-AzureResourceGroup cmdlet.