Is it possible to handle BCH transactions on Bitcoin Core wallet? I've installed Bitcoin Core on a server and it works well for BTC. I would like to know can I use the same server and platform to support BCH too?
I know that the addresses generated in Bitcoin Core are usable for BCH too. But how if I am able to handle BCH transactions in this machine, how can I differ them from BTC ones?

Thank you in advance for your replies.
If your BTC addresses aren't SegWit addresses, you can use dumpprivkey to extract your private keys and use them in a BCH wallet. You can import them to Electron Cash, which is a wallet software, or Bitcoin Unlimited/Bitcoin ABC, which are equivalents of Bitcoin Core. I'd advise against using BU/ABC and Core on the same machine, because both of them use the incoming port 8333. Besides, you might need to set datadir option otherwise they'd corrupt Core's blockchain and wallet databases.