What are some key attributes that an experienced PMM has or needs to get to SPMM?

As you move towards a more senior role, you'll find yourself working on multiple projects and launches at once. One of the most critical skills here will be prioritizing, getting you and your team organized and managing reasonable expectations for all stakeholders - basically taking a more strategic approach than focusing on individual tasks. 

The key differences in Sr PMMs and PMMs come down to ownership, self-sufficiency and complexity.

As a Sr PMM, you will be expected to self-sufficiently drive projects on your own without significant guidance from your manager. You will also be expected to be able to lead and own more complex initiatives than as a PMM and to work amongst more ambiguity to figure situations out. You are influencing at higher levels, not just contributing and taking orders.