Oh jeez...Networking is my weakness but I want to see if I can help. I know that each computer gets assigned different internal IP addresses based off of the network hub/router's ip address. I'm not familiar with L3 switches but unless that has its own seperate internal IP address, I don't think you can assign the computers hooked up to it using a different internal IP address as the one assigned from the router...oh wait, I see what you mean. Most likely you can't do that. Each computer uses only two/one specific IP addresses (one from the router and one from the WAN connection). Not sure HOW it uses both, most likely it assigns the IP addresse with multiple router IP addresses so more than one computer can use that internet connection...
Now...PLEASE tell me what I just said lol. If it doesn't make sense please don't question me. I left the part before the "...oh wait" because I didn't know what to take out lol. But most likely my answer is no.