SQL Connector for Azure Key Vault - multiple key vaults and keys per instance
In SQL Server 2016 Enterprise Edition, is it possible to link a single
  instance to more than one Azure key vault / EKM provider? If so, how
  would I add an additional provider? Any security considerations?


You don't add an additional provider, the provider is simply a reference to a DLL on the SQL Server that provides the interface to your EKM provider.

You add a credential to interact with the key vault (using the FOR CRYPTOGRAPHIC PROVIDER option) and associate that credential with a login. If you have additional key vaults, you add additional credentials and additional logins.


  Also, is it possible to encrypt each individual database with
  different encryption keys, or is the same encryption key used for all
  databases?


(Assuming you mean TDE) Yes. You create a database encryption key, scoped to the DB in question, protected by a certificate or server asymmetric key per database. You already get a different encryption key per DB and you can even protect the DEK using a different cert or asymmetric key per database.

Scenario:
I want to protect 2 databases with TDE using individual Asymmetric Keys provided by different Azure Key Vaults.

Steps:


Create Cryptographic Provider for Azure Key Vault
Create Credential1 for accessing AKV1
Associate Credential1 with sysadmin user
Create Asymmetric Key1 from AKV1
Create Login1 from Asymmetric Key1
Remove Credential1 from sysadmin user
Add Credential1 to Login1
Configure TDE on DB1 using Asymmetric Key1
Create Credential2 for accessing AKV2
Associate Credential2 with sysadmin user
Create Asymmetric Key2 from AKV2
Create Login2 from Asymmetric Key2
Remove Credential2 from sysadmin user
Add Credential2 to Login2
Configure TDE on DB2 using Asymmetric Key2