Does anyone know of any third parties that can enhance a Marketo form? Specifically I'm looking for the ability to embed a Marketo form where the user submits 2 fields, and then UPON COMPLETION of those fields is shown another screen with more fields. This is different from the existing progressive profiling, as I want additional fields/screens to show only once the initial form has been submitted. Basically, I want more flexibility in the layout of an embedded Marketo form.
Have you already looked into visibility rules for Marketo form fields? This would allow you to keep the process on one page and hide your secondary fields until both of the primary fields are filled out, and you can also change which secondary fields are shown based on the answers the person provides to the primary fields. More here: Dynamically Toggle Visibility of a Form Field - Marketo Docs - Product Documentation
Otherwise, it sounds like you need to ensure your first form's redirect rule takes the user to an additional page with another embedded form. I think I'm missing how this can't be accomplished with Marketo currently - if you have any more details that could help.
This can be accomplished using Javascript. Sanford Whiteman has provided excellent documentation and example in this thread: https://nation.marketo.com/message/214739-re-two-part-form-submittal?commentID=214739#comment-214739
Yes, this can be done--I personally do a variant of this using fieldsets to determine pages rather than multiple forms--but it does require some JavaScript development.