It does make sense. It may even be the case that even it could be only one person, he wanted to have two different signatures depending if he acts in two different roles! :lol:
I don't know if as a web mail it can have it, I haven't checked that, but since you can also activate POP access, and that's free, each of you could receive your mails in your regular e-mail client and use this client to have your personalised signature. Since you'll be using different computers and different clients, each of you can use a different signature.