Allow certain changes after digital signing

The changes allowed after signing depend on the P value of the DocMDP transform parameters or field lock parameters of the existing signatures:

(Optional) The access permissions granted for this document. Changes to a PDF that are incremental updates which include only the data necessary to add DSS’s 12.8.4.3, "Document Security Store (DSS)" and/or document timestamps 12.8.5, "Document timestamp (DTS) dictionary" to the document shall not be considered as changes to the document as defined in the choices below.
Valid values shall be:
1 No changes to the document shall be permitted; any change to the document shall invalidate the signature.
2 Permitted changes shall be filling in forms, instantiating page templates, and signing; other changes shall invalidate the signature.
3 Permitted changes shall be the same as for 2, as well as annotation creation, deletion, and modification; other changes shall invalidate the signature.
Default value: 2.

(ISO 32000-2 Table 257 — Entries in the DocMDP transform parameters dictionary)

Acrobat handles signatures without an MDP setting as a variation of the P-value 3, see this stackoverflow answer.

Thus, if the effective P value after A's signature is 1, you're out of luck. If it's 2 and you have prepared a button field as an image field, you can follow @try67's approach. If it's 3, you can alternatively use annotations for watermarking. 

I believe the only changes that can be allowed is filling in form fields, so you could use image fields for adding those stamps, instead of an actual stamp comment, and then it should work.