Depending on how you would want "sub-networks" to operate and interact with the main network, I would think that Proof-of-Burn could work as part of the transfer mechanism from the main network to sub-network.
AFAIK proof-of-burn is an one-way blockchain hop. I'm more interested in hopping without burning the bridges to return back. Kind of like people talk about side-chains and tree-chains; I'm thinking of DAG-chains or directed-acyclic-graph-chains.