SQL Server - Nonclustered Index with Include on User Defined Table Type?

I was working with in-memory User Defined Table Types and got stuck on creating indexes on them.

Here's what I am trying to do:

CREATE TYPE dbo.CustomersTbl
AS TABLE  
( 
        customerID int NOT NULL,
        customerName nvarchar(100),
        customerAddress nvarchar(100),
        customerCity nvarchar(100),
        customerEmail nvarchar(100)

        INDEX IDX1 NONCLUSTERED (customerID) INCLUDE(customerName,customerAddress,customerCity)
)

    WITH  
    (MEMORY_OPTIMIZED = ON); 

This works fine if I do not include the INCLUDE part.

If this were a standard table I would create the index with the INCLUDE.

So my question, is there a way to create that index on the User Defined Table Type with the INCLUDE, or would there be a reason why I would not even want to? I am using these table types to create in-memory table variables.

I am currently using SQL Server 2017.