Two accounts on one computer
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I cannot see any problem with that. You cannot be logged into two separate accounts simultaneously though.
However, be mindful not to leave an account open for someone else to just hop on and be used as their own. chess.com staff might be informed of the suspicous (even if innocent) behavior and cancel both.
Then you can sue. 
I am short on home computers right now and my son would like to play Live Chess. Could he create an account separate from mine, i.e., a different user name on the computer than I use to play Live Chess? Thank you.
BTW, I first tried having him play Yahoo chess on my computer, but then my computer caught a terrible malware virus (AV Security Suite) that took an expert to remove - and I do have the latest Norton Security! Beware of this malware virus, as it is current and can bypass Norton. Go to youtube for instructions on how to remove it.