If the employees will connect through the company's unbrella with a static IP or a narrow range of static IP's then you could check for that. Additionally, with an IP match, you could require just a password (no user name), i.e. a single password that the company distributes to the employees. You could give the company several passwords so that they could manage who had access and who did not by groups (for example, a visiting team could be given access for the time of the visit and then the password deleted bu you). You could also reassign passwords on a yearly basis, for whatever reason. They could use the company name, or nickname, as a user name if desired (You could expand to other companies).
Of course this assumes that more than one login from the same virtual user is not an issue with the operation of your site.
Gary