Can I save a PDF with an un-filled signature field, to send to multiple clients via my own email?

I am using Adobe Acrobat via the web-app.

So I'm just now learning about e-signatures via Adobe Acrobat. Thus far, I have learned how to add signature fields to a PDF, and I am able to send these documents to specific recipients directly from Adobe Acrobat.

However, what I would ideally like to do is create one form with a general signature field that could be signed by any client who may need to. I would like to be able to save this PDF locally, so that I can email it to clients via Microsoft Outlook while CC'ing my colleagues.

Or, alternatively, I would like to know how to add CC's when sending a PDF to a client via Acrobat. At the moment, I am able to add multiple recipients, but Acrobat assumes I am seeking a signature from all of them. Is there a way to request a signature from one party via Acrobat, while CC'ing my colleagues without the requirement of a signature from them?

Please let me know if any of my questions require clarification.

Thank you in advance for any help you may be able to provide.