You can't do multiple prereqs, but you can adjust them to make the weapons come after another line of research.
All you would need to do is change the Galactic Warfare 'Requires' tag from 'None', to whatever tech you want the weapons tree to come after.
It might actually be interesting to make, say, Xeno Ethics the prereq for Galactic Warfare. That way they would have to get Diplomatic Translators and Xeno Ethics before any weapons research could begin. They would be forced into choosing an alignment very early in the game.
Or they could be forced into researching the Research branch to a certain point, to ultimately make researching those weapons all the faster while forestalling the earliest wars.
I never thought of doing it that way, so thanks for the idea. It brings a new twist to the game.