Is there will be own DEX for cross-chain trading? Or just protocol? And why only for ERC tokens? They are not popular anymore. You should have more options
1. REN - it's not DEX, it's protocol for DAPPS/DEX/Darkpools.
2. REN (protocol) - can support with any chains , not only ERC 20. BTC/ZEC/ETH - chains that are already supported
You might want to read this:
1.
https://defiprime.com/ren2.
https://medium.com/renproject