Not really. There are some sites that have had that option and it has not been well-received by the bulk of members. However, we do not have a policy against having multiple accounts, for precisely this reason. You could open up a secondary account using a different email address and have it be anonymous.
I don't expect this to be a problem for you, but because I'm providing general information here that others may read, you cannot use a secondary account to break the rules. If you're using a second account to attack members, retaliate, or circumvent a break or ban, chances are all your accounts will be closed and you will not be welcome back. You also can't use a second account in a deceptive way. For example, if you are a man with one account and your second account is a flirty chick trying to lure people into online flings, I'm canning both your accounts. If you've had an issue with someone in the past and you rejoin as "someone else" to mess with them, your accounts are getting closed.
I'm all for privacy and I'm totally cool if people want a second account for sensitive issues or just to play with. Some people like to be characters and provide silly answers. That's fine. I draw the line when you're screwing with people/ catfishing.
Again, I don't think any of this is an issue for you, Neelie, but because I'm putting this out there, I want it to be crystal clear to others who may get the "ingenious" idea to have a second account for any type of nefarious reason.