Cosponsors to an amendment may be added or changed using the same amendment submission form originally used to submit the amendment if accessed by the same user.
AMENDMENT COSPONSOR CHANGE FORM
If unable to access the electronic form, amendment co-sponsors may be added or changed through a formal letter submitted by the office of the member sponsoring the amendment. The letter should be written on Congressional letterhead, detail the number of the amendment(s), the names of the members wishing to cosponsor the amendment(s), the underlying legislation, and should include the sponsoring Member’s signature.
The Cosponsorship Letter should be delivered as a PDF via e-mail to Rules.Amendments@mail.house.gov and followed by a phone call to (202) 225-9091 to confirm receipt. A template for a cosponsor letter can be found here