Internet Explorer can remember any number of user/password pairs, as long as you still have it set up so that it remembers/asks you whether it should remember the passwords.
Go to IE's 'Tools' menu, choose 'Internet Options', then choose the 'Content' tab. Towards the bottom click the 'AutoComplete' button and make sure that 'Username and Passwords on forms' is selected (you can even choose whether you can be prompted every time)
After the first time you fill in the form with your company's username and password it should remember these.. so the next time you start typing your company's username, it will popup below the entry field just like your username would if you had started typing yours, then upon pressing the down arrow key and tab the correct password will be filled in.
hope this helps