What if you're not a partner on the other platforms, can you still stream to Facebook, Youtube, Twitch, all at the same time? Smaller streams rely heavily on chat and interactions, but 1000+ viewer streams generally don't so you don't need to read 3 different chats. You can still receive donations and maybe ad money?
The streamer known as Destiny and Giant Bomb sort of do this. They stream on Twitch but they accept monetization through alternative means. Destiny is actually exclusive to Twitch, he just hosts his streams on his own website and accepts subscriptions and donations there in addition to Twitch, all of his chat is on his own website though. Giant Bomb is not monetized through Twitch, it's monetized through CBS Interactive and hosted on their own site, but the stream is a Twitch stream. So they're not on multiple platforms, but they've not tied themselves to Twitch's monetization.
Why do you think this would help? Going from 0 to 1 viewers on one platform alone is quite hard, and then again for 1 to 10 viewers. You would have to put in that effort for each different platform, and ultimately you would still need to pick one and ditch the others once you qualify for partnership
As was implied in my comment, I was thinking of larger streamers with thousands of viewers that don't rely on chat. Someone like Ninja who gets 100k viewers could get a couple thousands more off other platforms potentially.