While this isn't something I've personally done before, you might want to start by tracing the action that attaches the signature to the work object, to see what rules are responsible. Once you know that, you can review them to see if they can be customized to allow multiple signatures to be attached.
On reviewing the SR, we see that it was determined as a product enhancement. The enhancement ID is updated under teh Relates Support Case Number. Please work with your Pega Account Executive to take this further or to check the progress.
As Vikas stated, if you create multiple attachment categories for the different types of signatures (EmployeeSig, ManagerSig, HRSig) and apply the relevant Attachment Category to the Signature field you can have multiple signatures on a single work object.
The limitation is that only one signature can be associated to a Attachment Category on a single work object, so having all signatures of type 'File' will conflict with each other.