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There is a fact that nobody discuss: Scrum works well with co-located teams because the interaction between the Scrum team and stakeholders is crucial to the success of the project you. Indeed, it is a good advise to have Scrum team and Product Owner sitting close each other because the communication is better. On the other hand, we have to consider in which way Scrum should to be implemented in multinational companies that have several offices around the world but they share the same vision.
My best approach to deal with this huge challenge is the following: adopting Scrum in each country with co-located teams so you should be able to keep strong communication between all the stakeholders.
I used to work in a big multinational company that bought a Chilean company. As this company is using Scrum in each of its branches they hired me to coach new teams. One of the projects consisted in developing a software to a Peruvian client but the Product Owner was in Argentina and to add more complexity to the project the Scrum team was located in Chile. Furthermore, the manager that was dealing with the client was in charge of the Product Owner so the last won’t be able to take decisions by their own because he has to follow orders by his boss.
Once the Product Owner and his manager visited Chile and met with Scrum team members for several days. During that time team members developed in better ways because they have the Product Owner close to them so he only to talk to him for a couple of minutes reducing the delays for hours or even a day that was happening usually.
My challenge as a coach in that company was to struggle to change the mindset of the corporate because managers get used to order everything so nobody was the autonomy to decide by themselves. Indeed, most of the time their opinion were barely requested.
If you decide to use Scrum you have to empower the Product Owner to take decisiones, and Scrum Master to remove impediments and trust on the professional skills of team members to follow their technical advises.
Last but not least, I found the biggest difficulty to deal with Scrum in multi geography companies is to help them to change their mindset and reduce the bureaucracy that produce so many delays.