Try adding them as Digital IDs.  Then, on the form field signature block, you may select the preferred digital signauture.

Where has Initials gone ?   Cannot see it as a choice anymore!

I had to sign for four different people with Adobe, and the way i did the work around was to create stamps of their signatures and apply them that way.  Having said that, it isn't a "signature" in the eyes of the program, it is just an image stamped over the page. but i am not sure if that matters for you or not. 🙂 

If you disable the sync in the registry, each user can setup their own signature and it wont sync across devices logged into the same account. We have an IT admin that all our software purchases are registered to, but by disabling the registry sync, none of our signatures sync across the devices. We have no identified any other issues this causes. It is done on adobe 2020 std and pro. This must be done on each machine logged into the account: 

Disable Adobe Acrobat Document Cloud services. It disables and locks all service access except those features controlled by the other preferences below.

[HKLM\Software\Policies\Adobe\<product name>\<version>\FeatureLockdown\cServices]
"bToggleAdobeDocumentServices"=dword:00000001

This restriction is all about selling licenses.  Adobe will mem and haw about how they are protecting users but it BS.  Acrobat pro is alreadt too expensive and this restriction, again is BS.

is there a way to save more than 2 signature on acrobat?

Let me blow your minds Adobe community.  Yes, it sucks that there is no multiple signature saving option.  But, I found that if you have your signature saved as a PNG you can "INSERT PICTURE" and insert that file.  I would imagine it would work with a JPG as well.  The signatures we have saved in our office have an invisible background so there are no issues with it looking like a pasted rectangle.  I must sign for multiple project mgrs. & the CEO in my office so I am glad to find a workaround.  I hope it works for you!  ❤️

Create a "stamp" with the image file of the signature. 

A simple solution. Normally, when you choose either a signature or an initial, it is automatically saved by the program, until one deletes it and chooses another.  

Just make sure to uncheck the box  which asks if you want to save signature, see attached pic, and that's it. Now every time you want to sign a new signature, just go to your folder where you keep all your signatures, and when asked for an image, choose one.

You need to use Certificates in order to have multiple secure signors.  Here are the instrux. Colleen P. Trusler

OPEN ADOBE AND CHOOSE EDIT/PREFERENCES

Step One: Choose Signatures from the list of Categories

1.    Choose Identities & Trusted Certificates. Click More

2.    Choose Add ID

3.    Choose A new digital ID I want to create now, click Next.

4.    Choose New PKCS#12 digital ID File, click Next

5.    Add your information, including email and click Next.

6.    Set a password, write it down because you will need it each time you use the certificate.

7.    Click Finish.

Step Two: Apply your Digital Signature (Secure Certificate )

1.    Open the Document and Navigate to the Signature area

2.    Select the tool for Certificates: 

3.    Select Digitally Sign from toolbar.

4.    When prompted to draw the signature area, click OK

5.    Draw the area larger than needed.

6.    A pop up with your multiple signatures (certificates) will appear.

7.    Choose your signatory and click Continue.

8.    Tick the Box for Lock document after signing if this is the last person signing the document.

9.    Enter your password for this certificate in the red box. 

10.  Click Sign.

11.  Save the document with a name indicating that the document has been signed. 
(e.g., Agreement 3.22.22 Executed)