The ZeroLabs Tokenization Module already supports multiple blockchains but with no bridging functionality. Our cross-chain bridging strategy will be implemented in 3 stages.

Phase 0 - App-level

Initially, ZeroLabs supports multiple blockchains on the app-level only. We are able to tokenize Certificates on multiple blockchains, and users can show a preference to tokenizations on the blockchain of their choice.
More details can be found here.
Limitation: The Certificates are non-bridgeable between different blockchains.

Phase 1 - Centralized Bridging

ZeroLabs is currently working on a bridging solution to allow cross-chain bridging liquidity for different Certificates.
Certificates would be minted on a single (main) blockchain and then bridged to other blockchain when there's a demand for liquidity. Certificates claimed on a bridged chain will automatically be disabled/burned on the main blockchain.
This bridge will initially be run by ZeroLabs with the possibility to be decentralized in the future.

Phase 2 - Decentralized Bridging

In the long-term, the ZeroLabs research team is focused on decentralizing the bridges and allowing the owners to bridge their own NFTs as they with and claim on whichever blockchain the bridge supports.