You’re not banned – quite the opposite in fact. Having had an offer from office X will give you a boost when applying to office Y.
However, there’s still some obstacles such as language. If you want to get into the German office for example, you have to speak German (same goes for France, Italy, Spain, etc.). If you “only” speak English apart from your native tongue, you should consider Netherlands and Nordics.
Hence, be clear about which office you’re targeting and start networking. For that, you should absolutely leverage your offer and you could even ask your recruiter or the Partners you interviewed with if they’re willing to make an introduction. They should be!
Hope this helps. Best of luck!