- is fully compatible with Bitcoin network.mainnet
- is able to interface to the bitcoin mainnet
- can use transaction ID's of the bitcoin mainnet
- Network.Network-X process network.mainnet's transactions
Generally, the idea of "mainnet" is to define the blockchain that is being used.
To be "fully compatible", Network-X would have to have the same blockchain as bitcoin, but if it did that then it would be mainnet. It wouldn't be a separate network.
If it does not have the same blockchain, then it is a separate network, but it can't be "fully compatible" with mainnet.
Perhaps you are suggesting nodes that hold two blockchains? They have BOTH the bitcoin mainnet blockchain AND a separate blockchain? In that case, they could "process" bitcoin transactions on the bitcoin network, and they could process Network-X transactions on Network-X. They would NOT be able to apply Bitcoin transactions to Network-X, nor would they be able to apply Network-X transactions to the bitcoin network. A wallet or service with such functionality would need to keep track of each balance separately. This exists in every exchange that accepts both Bitcoin AND Litecoin. In that case Litecoin would be "Network-X" in that the transaction structure is the same, but uses a completely separate blockchain, and the exchange keeps track of BOTH Bitcoin and Litecoin blockchains.