To put Joeri’s answer into context, have a look at the Adobe technical white paper Adobe Acrobat 9 Digital Signatures, Changes and Improvements, especially its section “Allowed and disallowed changes.” Here Adobe clarifies the allowed changes (as seen by Acrobat 9 and up) that can be made to a certified or signed document without invalidating the signatures applied to the document.
Allowed actions for certified documents
Certified with no changes allowed
Allowed
- No changes allowed
Disallowed
- Digitally signing
- Supplying form field values
- Adding or editing annotations
- Adding form fields
- Changing page content
Certified with form fill-in and digital signatures allowed
Allowed
- Supplying form field values
- Digitally signing
Disallowed
- Adding or editing annotations
- Adding form fields
- Changing page content
Certified with annotations, form fill-in, and digital signatures, allowed
Allowed
- Adding or editing annotations
- Supplying form field values
- Digitally signing
Disallowed
- Adding form fields
- Changing page content
Allowed actions for signed but uncertified documents
Allowed
- Adding signature fields (see Limitations on adding signature fields to signed but uncertified documents)
- Adding or editing annotations
- Supplying form field values
- Digitally signing
Disallowed
- Adding form fields other than signature fields
- Changing page content
As you see “Changing page content” always is in the “Disallowed” category. As adding a page changes page content — afterwards there is at least a white page where there used to be nothing —, this is not allowed.
(Even though not explicitly mentioned here, instantiating page templates most likely also is allowed whenever form fill-ins are allowed as that would conform to the PDF standard, cf. ISO 32000-1 section 12.8.2.2.2. But making use of such page templates would at least require the document to be specially prepared before signing, and your question sounds like the documents are already signed without any such preparation…)
PS: Obviously even these allowed changes need to be added in append mode aka incremental updates. Anything else will break the signature for good. For some backgrounds see this answer.