New one for me: Customer wants us to NAT a host to particular IP over a VPN tunnel (ASA) that's also in another customer's tunnel. Possible?

So we have a server that external customers access over site-to-site tunnels with is true IP.

A new customer wants to establish a tunnel with us but wants us to NAT the server IP as it goes out to something specific for them. Is it possible on a Cisco ASA to NAT an IP for only one specific tunnel and not others?

My pushback was for them to NAT our IP on their side as it comes in (not sure what device they have yet, waiting for that info)