This is fantastic and addressed my problem!  Thanks Tanner for your brain power on this!

I had a little trouble with it so I created a step-by-step cookbook  based on the original post and additional comments for my benefit.  Maybe it will be a help to someone else:
 

Adding an Approval Process with four or more buttons
1.  Open Forms 
2.  Go to Design Mode (New Form + Form Approval template)
3.  Edit the Form that needs a 4th or more button (ex. "Starting Form")
4.  Click the Custom HTML to add that field to the canvas.
5.  Remove the test "Enter the text you want this field to display"
6.  Click the Html tab
7.  Go to the beginning of the line and paste the following:
<input type="submit" class="newButton action-btn Submit" value="Hold" aria-labelledby="action" name="action">
8.  Go to the ending of the line and remove the following:
<p><br></p>
9.  Replace the variable in value with the name of the button that you are adding (ex. "Hold")
10. Click Done  -  you should now see a button on the canvas with the name that you gave it.
11. Click the "CSS and JavaScript" tab at the top of the canvas.
12. Click in the JavaScript section and past the following:
$(document).ready(function(){
  //Moves button from form to lower button wrapper and removes DIV that button was housed in
  $('.newButton').detach().appendTo($('.button-wrap:first'))
  $('#q2').remove();
})  
13. Click the "Save" button

At this point the new button(s) will not show for the originator - only the "Submit" button (discussed below).

Changes to the Process Diagram
1.  Click Process Diagram
2.  Create a User Task from the "Message Start Event"
3.  Double-click the User Task to show the details
4.  Under the General tab name the process (ex. "Approval") and assign users or groups for the approval
5.  Click the Form tab & select the form that you were working on (ex. "Starting Form)
6.  Select the Action Buttons that you want to show 
7.  Click the Outflows tab and add the condition for each button.
8.  Click the User Task (ex. "Approval") 
9.  Click the arrow and select "Gateways" - then "Exclusive Gateway"
10. Click the Exclusive Gateway that you just created and add an outflow (ex "End Event")
11. Double-click the Exclusive Gateway and select outflow.
12. Add a Path Name (ex. Hold) the add the text "Hold"
13. Click the Conditional Expression & add the name of the button (ex. "Hold")
14. Click the drop-down and select "Last User Action" then click Insert
15. Edit the condition from: /dataset/_fs_action=""  to /dataset/_fs_action="Hold"
where "Hold is the name of the button.
16. Double-click the User Task (ex "Approval") & click on the Outflows tab
17. Edit the condition from: /dataset/_fs_action=""  to /dataset/_fs_action="Hold"
where "Hold is the name of the button.
18. Click Save
19. Click "Process Options" under Setting and select "Published"
20. Click Save

Test - Start the process (the form) and click "Submit"
Have the user assigned to approve go to their Forms Inbox and select this test form.
The form will display with the additional button(s).

Note:  if you wanted an additional button so that the originator can select a choice other than 
       Submit( the submission form), follow the above steps but modify step 12. Click in the JavaScript section and past the following:
$(document).ready(function(){
  //Moves button from form to lower button wrapper and removes DIV that button was housed in
  $('.newButton').detach().appendTo($('.btn-wrapper:first'))
  $('#q2').remove();
}) 

btn-wrapper is used for the initation form.
button-wrap is used for the user task (approval) form.
 

Would it be possible to get you to walk me through this process of adding a fourth Action Button to my form?

Dawn

I am tying to do this on the initiating form and it's just terminating when I click the added button or the default submit button and I'm not sure why. At first I thought it could because I had set up a 'normal' button on the second stage with the same value. So I changed the value from "Save to Repository" to "Save to Repo" to make sure the two buttons did not conflict with each other but It still is not working. I am using the default submit button and named it "Save Progress"

What they are wanting is if a team member is entering the data they have the option of saving directly to the repository or saving the progress and making the form available for another member of the team to pick up and add to the form.

My custom HTML

<input type="submit" class="saveToRepoButton action-btn Submit" value="Save to Repo" aria-labelledby="action" name="action">

My JavaScript (note I commented out the call that would be used if it was not an initial submission form)

$(document).ready (function () {

  /************************************************************************************/
  /*                      START: Move Additional Action Button                        */
  /* https://answers.laserfiche.com/questions/167540/Additional-Action-Buttons#183898 */
  /*                                                                                  */
  /* Moves button from form to lower button wrapper and removes DIV that button was   */
  /* housed in                                                                        */
  /************************************************************************************/
  /* used for initiation/submission form */
  $('.saveToRepoButton').detach().appendTo($('.btn-wrapper:first'));
  
  /* used after initiation/submission form */
//  $('.saveToRepoButton').detach().appendTo($('.button-wrap:first'));

  $('#q271').remove();  
  
  /************************************************************************************/ 
  /*                       END: Move Additional Action Button                         */
  /************************************************************************************/ 

}); /* END: $(document).ready (function ()*/

Image is how I have the action set up

If I remove the added button my submit(Save Progress), works as expected and sends the from to the next step.

EDIT:

I'm not sure if this could be causing the issue but my form is a pagination form and I'm showing the buttons on each page using the code below

  /*******************************************************************************/
  /*                       START: show buttons on each tab                       */
  /*******************************************************************************/ 
  function showButtonWrapper() {
    /* used for initiation/submission form */ 
    $('.btn-wrapper input[type=submit]').removeClass('hidden');
    /* used after initiation/submission form */
    //$('.button-wrap input[type=submit]').removeClass('hidden');
    
  };  
  
  /* next button clicked */
  $(document).on('click','.cf-next-btn ',function(){    
    showButtonWrapper()
  }); 

  /* Previous button clicked */
  $(document).on('click','.cf-prev-btn ',function(){    
    showButtonWrapper()
  });
  
  /* tab clicked */
  $('.cf-pagination-tabs li').click(function(){
    showButtonWrapper();
  }); 
  
  $('.cf-pagination-tabs li').eq(0).trigger('click'); 
  /*******************************************************************************/
  /*                        END: show buttons on each tab                        */
  /*******************************************************************************/

Thank you for this info.  I applied your code but I have an issue.  When I go to configure the Sequence Flow, the Action is not listed.

Addendum - sometimes the div class to identify the buttons is "button-wrap" instead of "btn-wrapper."  This appears to be the case when working off a user task vs. an initiation form.