I need to amend my 2023 return changing it to allow someone else to claim me, even though I filed married filing separate

Are you sure someone can claim you?  Who?  Your spouse cannot claim you.  Did you get married and your parents can still claim you?  

And why are you filing Married filing Separate?  Joint is almost always better.  There are several credits you can't take when filling MFS.

But yes you can amend if your return was accepted or mailed.  Or is your return rejecting because someone claimed you?  Or is their return rejecting? If their return rejected they will have to mail their return even if you amend.  So they don't have to wait for you. 

You should not amend until the first return has fully processed and you get the first refund or your tax due payment has cleared.  

How to Amend this year

https://ttlc.intuit.com/turbotax-support/en-us/help-article/tax-return/amend-federal-tax-return-current-year/L7eS6o1qh_US_en_US