As a single if you make more than $131k you can't use a Roth IRA. If you're married, your combined income has to be less than $193k for a Roth IRA.
If you're making too much to contribute to a Roth IRA, then you won't qualify for the ability to deduct your Traditional IRA contributions from your taxable income.
So after maxing out the 401k, I would just sock it away in a taxable brokerage account using index funds like you mentioned.