Cable modems and additional DNS Suffixes

I recently obtained a @Home network cable modem and use Secure Remote VPN software to connect to my employers network. Secure Romote monitors request sent to computer.mycompany.com and then prompts for a login. My cable modem uses DHCP to configure DNS, is there a way to add mycompany.com as a last resort DNS suffix without interfering with my internet connection. If not is their a way to add the 5-10 servers I use to a host file that would map computer to computer.mycompany.com? (I am not too familiar with host files or DNS) Thanks for the help.