Automatic Azure/365 Group Assignment

The existing groups at my company are a little messy, with a mix of 365, security, and distribution. What I would like to do is set up groups to automatically add users based off their department or job title, and then add them to the existing groups without further input by me.

I can set up the dynamic membership rules just fine, for example Job Title and Department containing Finance or Accounts grabs me the whole finance team. I'd like the members of this new group to then be thrown into the existing groups by creating a rule or config if that's possible.

Nesting the security group into the existing security groups works, but I know I can't use that method with 365 groups. Is there an overarching rule or work-around I can use for this?

Worst case I will dynamic rule the existing assigned memberships, but given the number of groups that'll take a while