It is possible to have a signature for new mails, and a different signature for replies and forwarded messages. All new mails will have the New Signature and all Reply or Forward mails will use the Reply/Forward signature associated with the New Signature.
It is important to note that this applies to any Reply message, if for example you are sent a new mail and you Reply (even though this is your first mail) the Reply signature will be applied. This works in the same way as New and Reply/Forward signatures do in Outlook.
To use this function you need to choose the Signature you would like to associate a Reply signature to.
If not all staff would like a Reply signature then you should duplicate the existing signature and amend and assign the new version as explained here.
This is done by editing the signature you want to use on new mails and then selecting the additional Reply / Forward signature from the dropdown list in the “Signature Properties” section:
Both signatures will then display on the sender edit form as shown below: