It's technically possible to do so, by editing the SAM database (under
HKEY_LOCAL_MACHINE\Security in the Registry), but it requires understanding of the binary formats used there. There exist tools that do this, such as NewSid – although it usually did the opposite of what you're looking for, but nevertheless it was able to change the machine SID and user SIDs, computer-wide. The NewSid webpage has some information on how this is done.
However, it won't achieve much. The SID is only used locally. It does not matter what SID you have; it will not give you access to any additional network resources. (This is similar to the arguments given by SysInternals when they discontinued the NewSid utility – it would create a fresh machine SID if you had cloned machines with identical SIDs, but it was explained that having identical machine SIDs, and therefore identical user SIDs, has zero effect on network security.)
For network authentication, Active Directory uses Kerberos and sometimes the (now-deprecated) NTLM, both of which authenticate users using their password or similar credentials.