Okay, so this has been done to death, but I am a sucker for punishment, I guess. The challenge I present to you, venerable posters of Alternate History, is provide Austria - Hungary with a piece of the colonial pie! Handwavium, the internal political scene is much calmer than it was historically, allowing Austria to have a more vocal international presence.
To begin with, I will suggest that the deal to purchase the Nicobar Islands goes through in this TL, since the Hungarians won't be able to screw it up. Perhaps they could get British Somalia at the Africa Conference if the Brits decide they don't really need or want it? Or perhaps they can be persuaded to sell it afterwards?