YES, Chess.com allows each member to have TWO accounts, with approval from support. Without support approval noted on the account, this is still considered cheating. If it's just a new username you are after, please see here.
Reasons to have a second account
There are many reasons you may want a second account. Some people prefer to test out new openings on an account where they don't have to worry about their rating, or you may want to keep certain games private. Or you may want an account just to play on when it's late at night and you're tired. Or any number of reasons! But there are also things you should NOT do on your second account.
Rules for two accounts
If you have two accounts, you may NOT:
Play the accounts against each other, even in unrated games
Play or spectate in the same vote chess game with both accounts
Play or spectate in the same 4 player chess, or other variant game with both accounts
Play in the same tournament with both accounts
Comment with both accounts in the same forum thread or discussion
Use the account as a 'speed run' account
Create the second account with a much lower rating than your main account
Other things to note
Memberships do not transfer to the second account. If you want to access your membership on both accounts, you must pay for it on both.
If you break the rules on one account, both accounts will be affected- If you are abusive on one account, and get muted, both accounts will be muted. If one account is closed for cheating, the other will also be closed.
Any attempt to coordinate both accounts in order to abuse, harass, or upset another member will lead to both accounts being closed.
In some special cases a third account may be allowed. If you are requesting a third account, please write to support before creating the account, and before using the below form. Note that third accounts are much less likely to be approved.
Creating the second account
If you want a second account, you may create one now. But before you use the second account for anything, you must request the account be approved for use.
When creating your account, please select a starting experience level as close as possible to your true rating:
New to Chess = 400, Beginner = 800, Intermediate = 1200, and Expert = 1600
If your rating is over 2000, please note this in the form below.
Please get in touch with us if you would like to make an alternate account.
If you are a Titled player please use the Titled Verification Form to request your alternate account.
If your account has been closed due to a Fair Play violation and you want to apply for a new account, please instead use the New Account Application Form here.
Speed run accounts are not allowed!
If you've watched the popular chess streamers for any amount of time, I'm sure you've seen at least one of them doing a 'speed run' using a new account to climb the ratings as quickly as possible.
This kind of thing is normally not allowed and is a form of cheating we call 'rating manipulation' or 'sandbagging.' Doing this yourself is a quick way to get your account closed!
However, streamers partnered with Chess.com have a special exception to this rule for entertainment purposes. The speed run accounts are closely monitored by the Fair Play team, and all points lost to the accounts are returned to the opponents.
The accounts are also often clearly labeled for anyone playing against them to see, for example here is the profile of one of Hikaru Nakamura's speed run accounts:
This kind of thing is not allowed otherwise, and only happens with special approval from Chess.com staff. Please do not make your own 'speed run' account or you will end up with it, and your normal account both closed for cheating!