can I amend a processor agreement that has already been signed

Yes, you can modify it as long as both parties agree

A signed data processing agreement is not a document that becomes fixed after signature until the end of the collaboration. Just like any other contract, both parties can decide together to make changes: add a new sub-processor, modify a retention period, or tighten agreements because something in the collaboration has changed. As long as both parties agree to the modification, there is nothing preventing you from revising the agreement.

What matters is that the agreement continues to meet what Article 28 of the GDPR requires. If the way a vendor processes data changes, a new party joins as a sub-processor, or the purpose of processing changes, that is often precisely the moment when what a data processing agreement must contain becomes relevant again: the existing text may no longer cover the new situation. You can record a modification with an amendment, a new annex, or by signing the entire agreement again — the form is less important than both parties documenting in writing what has been agreed.

Where this comes from: Article 28 GDPR

Article 28 of the GDPR specifies which topics a data processing agreement must cover, but does not state anywhere that a signed text cannot be modified later. The EDPB guidelines emphasize above all that the content of the agreement must continue to reflect the practice of processing — if that practice changes, it is logical that the agreement evolves with it. An agreement that has not been drawn up at all carries a different risk than an agreement that is updated; what the consequences of that can be is described under what happens if there is no data processing agreement with a vendor. Also, a modification that is only agreed by email raises the same question as with the first contract: whether that is sufficient is described under can a data processing agreement also be agreed orally or by email.