Is it possible to nest html forms like this
so
You can also use formaction="" inside the button tag.
<button type="submit" formaction="/rmDog" method='post' id="rmDog">-</button>
This would be nested in the original form as a separate button.
As Craig said, no.
But, regarding your comment as to why:
It might be easier to use 1 <form>
with the inputs and the "Update" button, and use copy hidden inputs with the "Submit Order" button in a another <form>
.