What comes after head of PMM, e.g. if you want to move to VP of a marketing team, how to do that? And how to ensure that you're getting knowledge of other marketing functions (e.g. paid) so that you are equipped to lead an entire marketing team (vs. just a PMM discipline)?

The great thing about being in product marketing is that it's a discipline that, by nature, is quite broad in strategic thinking and interacts with the key go-to-market functions in a business. This gives you a huge advantage if you can craft your story to be a VP of marketing! 

Broadly speaking, I think this reflects any kind of process for making a job change. 

1. Understand the VP Marketing role: Are you looking to go to a smaller company and be their first hire? or perhaps the first leadership hire above a small team of 1-3 people? If so, you'll need to roll up your sleeves and do everything from continuing product marketing to brand to demand gen to marketing operations to events and technology decisions. The most common things I've seen are moves from PMM at a large/mid-sized company to VP Marketing at a much smaller organization and then laddering up those skills over time to move to larger and larger companies.
2. Take inventory: Figure out what this theoretical VP Marketing role entails and look at your own skills. What gaps do you have? What experiences do you need? 
3. Fill the gaps: Here's where you need to be proactive and find opportunities within your responsibilities and leverage the relationships you have. Are you running a campaign? Try to do your own SEM using online tools (there are a million tutorials online on how you can experiment with this). Trying to do ABM? Learn how to run reports in Salesforce to find your target audience. Doing some naming? Spend time with the brand team to understand how brands are created and sustained. If you don't have these teams, and even if you do, be sure to read and talk to experts to understand the tasks and challenges of different facets of marketing.

To acquire the job you have to put yourself out there - make a resume that is for VP Marketing roles. Say you're looking for new opportunities on LinkedIn. Apply for roles. Talk to recruiters. Fail. Get feedback. Fill the gaps. Apply again. Eventually, you'll land the role and it will put you on a very steep learning curve! 

First of all - I don't think you HAVE to become a VP of Marketing from Head of PMM. You can choose to take on bigger PMM roles at bigger companies. 

That said, I've made the move to be a VP of Marketing at an earlier-stage company. I personally believe that PMM leaders make great VPMs for certain businesses - especially ones that have a mid-market or enterprise sales motion, require category creation or are in crowded markets (and will rely on differentiation). 

While in the Head of PMM role, make sure you really partner closely with the Head of DG. You are uniquely positioned to think through the audience (which is targeting), the value proposition (which is the campaign theme or message) and the offer to build a trusted advisor relationship (a compelling call-to-action). 

For the rest - you need to demonstrate that you will be GREAT at hiring, especially for your weaknesses. There's actually strength in that. :) 

Product Marketing could be under Marketing or Product depending on the organization. The good thing about a Product Markering role is that the role, by its nature, interacts with many different parts of the business, from Sales to Marketing to Product, so Product Marketing gives you an opportunity to see how the organization works beyond product marketing and prepares you well for leadership roles accross the organization.

Lots of things can come after VP/Head of Product Marketing. It’s not just about a linear path. Depending on the size of your company you can take on additional teams adjacent to product marketing such as content marketing, social, research, customer marketing. You also don’t necessarily need to lead new teams to learn about them. You should be learning about all aspects of marketing (how to drive pipeline, optimize conversion, develop content and events) in order to figure out how to drive the growth of your product/company.