Is it normal and still proper (in agile/SCRUM-based software development) for a product owner to be in charge of more than one product?
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The important part is to have a product owner in each team who has the right mix of skills, responsibilities, time. If a single person can fill the role for two teams, there's nothing wrong with that.
On the practical side, once you have 5 or 10 people on a development team there tends to be more than enough work to keep a product owner busy. The specific number will vary based on the kind of products you build and how you divide the work.
Practicality may dictate that one person serve as the product owner in some circumstances, especially in related projects where one person with a high-level view of both can help the two teams to coordinate and learn from one another's mistakes, etc.
However, you need to beware of the costs of multi-tasking. If someone is constantly having to switch contexts between unrelated projects, they are probably not going to get nearly as much accomplished as if they were able to focus on one product at a time.