Yes, you can do it in IIS of Windows 2000 Server easily.
I have been doing it many times.
After you create the new web site, right click the site to go to Properties, click Advanced... button at the right of IP Address box,
then click Add... to add a Host Header. The host header is the domain name that tells IIS which site to retrieve (since many sites share one IP). Tips: one web site can have mutliple domain names too by adding more Host Headers.
The only drawback is you can't browse the site by using IP such as
http://123.123.123.123. Without the host header, IIS doesn't know which site you want to access. Another thing is you can't use this single IP to setup multiple ftp sites. IIS doesn't support multiple ftp servers to sit on one IP (can't add host header too). You can use one ftp site for all customers, then create mutliple virtual directory so the customers can logon and be mapped to their individual wwwroot (also their ftproot).
I am not sure whether Windows .NET can support multiple ftp host header. You may check it out.
Hope this helps.