MegaMenu: looper children

I’m trying to create a 3 tiered megamenu using a single menu as the provider source. Other than my previous tickets, I’m not finding a lot of documentation on how to set this up.

I’ve been able to setup the second tier using:
{{dc:looper:field key="children"}}

I’ve managed to list the first set of the third tier, but cornerstone ended up throwing an error… and I lost my progress and haven’t been able to recreate it.

How would I setup the third tier? Would this be the provider?
{{dc:looper:field key="children.0.children"}}

Am I approaching this correctly?