Glad you've been thinking about this! So far this is the only post/article I've found exploring the topic specifically from the European perspective. 

I imagine it to be easier if the international network initially runs under the name of one individual national organization.

I'm a bit skeptical of this. Wouldn't you think that such international network/organization might not gain as much traction if it used the name of a national one, since it would be kind of misleading?

What do you think would be the best course of action if a national organization wanted to scale up into an international one, without sacrificing the original national organization completely? What could a successful branching out process look like? Supposing that creating a new organization would miss out on some of these benefits of scaling up you mention here.