A few years ago, I wrote about how to scale a blockchain by having multiple derived blockchains (sidechains), keeping the sync between the parent blockchain and the derived ones. Read: Connecting Blockchains (7).
I also gave a talk about connecting different blockchains at LaBitConf 2016 (Buenos Aires). Some ideas in my Connecting blockchains post series. The idea of having many sidechains could be read at Multiblockchains.