Can an organization have multiple products
The company I work for started Scrum 3 years ago with one Agile Scrum Team. It has one Scrum Master, one Product Owner, and one Development Team. The product they work on is the company's mobile app. The product is still active today, therefore, so is the Scrum Team.
A few months ago, the company realized the need to create a new Agile Scrum for an existing website, taking it from waterfall to agile. It has a different customer base than the Mobile App. That's why it has it's own Agile Scrum Team, also having one Scrum Master, one Product Owner, and one Development Team. The product they work on is one the company's websites, which again, reaches a different customer base than the mobile app.
Is it within the Scrum Framework for an organization to work on different products at the same time and, therefore, have different Scrum Teams?
The Scrum framework works for many teams. A company that only has 1 product is rare in this day. That would be a very small company by today's standards. In every company that I have worked that used Scrum, or even Scrum-like practices, had multiple products.
The Scrum Guide states this as the opening to the Definition of Scrum section.
Scrum (n): A framework within which people can address complex adaptive problems, while productively and creatively delivering products of the highest possible value.
Notice the pluiral for problems and products. No where in the Guide does it say that all those products need to exists at different companies. As long as you can define a Product a Scrum Team can exist. In your companies case it seems that they have been able to define more than one product.
I say go forth and Scrum. And help them find a third or fourth product that can benefit from the framework.
Yes. And if a single product, like an app, became too large and complex, that could be divided up into components or smaller products, each with their own pod, or Scrum Team. Personally, my inspection has shown me that more than three developers in one team is too many. So I prefer many smaller teams over larger eleven-person Scrum Teams.