Is there a way to have a field created on a form based on completion of another field or use of a button

Can you explain your use case?  That perceived need is highly unusual.  There is likely a better solution.

Say I have a form that requires approval on a case by case basis from anywhere to 1 to 12 users. Is there a way that when user field 1 is populated I have the option for user field 2 to appear on the form? And so on?

OK, so you don't want to create new fields on the fly, just expose them.

No problem

So you can have a form rule that says
When approval 1 is not blank, show approval 2

Then another for rule that says
When approval 2 is not blank, show approval 3

etc up to 11 rules in total

Yes that works, but the ability to create new fields on the fly would also be useful. Is there a way that is possible?

It does not make sense in Quick Base to create new fields on the fly so I hesitate to explain how it could be done. 

It is just not good design to be generating new fields willy nilly.  It means that you actually need to have a child table to hold the data, so it's a design issue of the tables and relationships that we should discuss.

I prefer to discuss the use case and we will come up with a proper design for the tables and their relationships.

Here is an overview of one project I'm trying to accomplish. 



Blue circle = User field
Red circle = Text- Multiple Choice field
Black circle = Text- Multi-line field


In this form the project manager could need only 1 approval could need 6 or more. The sign off and comment fields are only editable by the user set in the respective approval field. The user is notified via email when they are assigned to an approval. There are other tables and forms within this app that need to remain view-able to users in the approval fields. 

Things I need to happen:
1. Project manager is notified via email when all assigned approvals are complete. Needs to be 1 email only not an email for each approval
2. Blank approvals(and corresponding fields) need to be hidden, but the approval fields still need to be editable by the project manager at all times

On this forum I can try to answer specific questions.  Or else I offer one-on one consulting services  and I can be reached via the contact information on my website QuickBaseCoach.com

I'm not sure if you have a specific question at this time.  The question seems to have evolved morphed from how to create new fields on the fly to an outline of the broad goals of your app.

If I could create new fields on the fly my problems would be solved ;)

Truthfully and speaking from working with Quick Base since 2002, if you create fields on the fly your app would be a nightmare.  There is a difference between exposing existing fields to users on the fly with form rules and actually creating new fields on the fly based on user input.

Over a period of time the number of fields would be too large and will slow down your app and the form. Like Mark suggested, you should figure out the maximum number of field you will possibly need and show/hide them based on the user input via form rules.