Multi tenant rate throttling for external resources

The solution I'll try

For the part where I expect the load to become problematic I'll do the following;

Each tenant will have their own resource group which will contain a 

Queue

Function

API gateway

The API gateway will be in front of the external system and will take care of the rate-limiting for the function. This could create a possibly high reprocess rate from the queue (and I'd pay to fail a request I'm paying for). I'd limit the function from scaling as well, but the only way to get fine-grained control is to put in an API gateway.  

This will only work for so many tenants as I'd hit limits on resource groups and functions. 

I'm not thrilled with this solution, but it looks plausible.